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The Chronux Manual
Peter Andrews
Hemant Bokil
Sumanjit Kaur
Catherine Loader
Hiren Maniar
Samar Mehta
Partha Mitra
Hariharan Nalatore
Ramesh Yadav
Ravi Shukla
August 16, 2008

Contents
Contents

i

1 Chronux Overview
1.1 Introduction . . . . . . .
1.2 Installation and Setup .
1.3 Documentation and Help
1.4 Chronux Organization .

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2 Spectral Analysis Toolbox
2.1 Data Formats and Parameters
2.2 Examples . . . . . . . . . . .
2.2.1 mtspectrumc . . . . .
2.2.2 mtspecgramc . . . . .
2.2.3 coherencycpt . . . . .
3 Locfit
3.1 Data Format and Parameters
3.1.1 Local Regression . . .
3.1.2 Local Likelihood . . .
3.1.3 Model Selection . . . .
4 Function Reference
4.1 CrossSpecMatc . . . .
4.2 CrossSpecMatpb . . .
4.3 CrossSpecMatpt . . . .
4.4 binspikes . . . . . . . .
4.5 change row to column
4.6 check consistency . . .

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CONTENTS
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
4.19
4.20
4.21
4.22
4.23
4.24
4.25
4.26
4.27
4.28
4.29
4.30
4.31
4.32
4.33
4.34
4.35
4.36
4.37
4.38
4.39
4.40
4.41
4.42
4.43
4.44

chronux . . . . . .
coherencyc . . . . .
coherencyc unequal
coherencycpb . . .
coherencycpt . . .
coherencypb . . . .
coherencypt . . . .
coherencysegc . . .
coherencysegcpb . .
coherencysegcpt . .
coherencysegpb . .
coherencysegpt . .
coherr . . . . . . .
cohgramc . . . . .
cohgramcpb . . . .
cohgramcpt . . . .
cohgrampb . . . . .
cohgrampt . . . . .
cohmathelper . . .
cohmatrixc . . . . .
cohmatrixpb . . . .
cohmatrixpt . . . .
countsig . . . . . .
createdatamatc . .
createdatamatpb .
createdatamatpt . .
den jack . . . . . .
dpsschk . . . . . .
evoked . . . . . . .
extractdatac . . . .
extractdatapb . . .
extractdatapt . . .
findpeaks . . . . .
fitlinesc . . . . . .
ftestc . . . . . . . .
getfgrid . . . . . .
getparams . . . . .
isi . . . . . . . . .

ii
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CONTENTS
4.45
4.46
4.47
4.48
4.49
4.50
4.51
4.52
4.53
4.54
4.55
4.56
4.57
4.58
4.59
4.60
4.61
4.62
4.63
4.64
4.65
4.66
4.67
4.68
4.69
4.70
4.71
4.72
4.73
4.74
4.75
4.76
4.77
4.78
4.79
4.80
4.81
4.82

jackknife . . . . . . . . . . .
locdetrend . . . . . . . . . .
locsmooth . . . . . . . . . .
minmaxsptimes . . . . . . .
mtdspecgramc . . . . . . . .
mtdspecgrampb . . . . . . .
mtdspecgrampt . . . . . . .
mtdspectrumc . . . . . . . .
mtdspectrumpb . . . . . . .
mtdspectrumpt . . . . . . .
mtfftc . . . . . . . . . . . .
mtfftpb . . . . . . . . . . . .
mtfftpt . . . . . . . . . . . .
mtpowerandfstatc . . . . . .
mtspecgramc . . . . . . . .
mtspecgrampb . . . . . . . .
mtspecgrampt . . . . . . . .
mtspecgramtrigc . . . . . .
mtspecgramtrigpb . . . . . .
mtspecgramtrigpt . . . . . .
mtspectrum of spectrumc .
mtspectrumc . . . . . . . .
mtspectrumc unequal length
mtspectrumpb . . . . . . . .
mtspectrumpt . . . . . . . .
mtspectrumsegc . . . . . . .
mtspectrumsegpb . . . . . .
mtspectrumsegpt . . . . . .
mtspectrumtrigc . . . . . . .
mtspectrumtrigpb . . . . . .
mtspectrumtrigpt . . . . . .
nonst stat . . . . . . . . . .
padNaN . . . . . . . . . . .
plot matrix . . . . . . . . .
plot vector . . . . . . . . . .
plotsig . . . . . . . . . . . .
plotsigdiff . . . . . . . . . .
psth . . . . . . . . . . . . .

iii
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91
92
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106
108
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111
112
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118
120
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124
126
128
130
131
133
135
137
139
141
143
145
147
149
150
151
152
153
154

CONTENTS
4.83
4.84
4.85
4.86
4.87
4.88
4.89
4.90
4.91
4.92
4.93

quadcof . . . . . . . . .
quadinv . . . . . . . . .
rmlinesc . . . . . . . . .
rmlinesmovingwinc . . .
runline . . . . . . . . . .
specerr . . . . . . . . . .
spsvd . . . . . . . . . . .
sta . . . . . . . . . . . .
staogram . . . . . . . . .
two group test coherence
two group test spectrum

Bibliography

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Chapter 1
Chronux Overview
1.1

Introduction

Neuroscientists are increasingly gathering large time series data sets in the
form of multichannel electrophysiological recordings, EEG, MEG, fMRI and
optical image time series. The availability of such data has brought with it
new challenges for analysis, and has created a pressing need for the development of software tools for storing and analyzing neural signals. In fact,
while sophisticated methods for analyzing multichannel time series have been
developed over the past several decades in statistics and signal processing,
the lack of a unified, user-friendly, platform that implements these methods
is a critical bottleneck in mining large neuroscientific datasets.
Chronux is an open source software platform that aims to fill this lacuna
by providing a comprehensive software platform for the analysis of neural
signals. It is a collaborative research effort currently based at Cold Spring
Harbor Laboratory that draws on a number of previous research projects
[1, 2, 3, 4, 5, 7, 8, 9]. The current version of Chronux includes a Matlab toolbox for signal processing of neural time series data, several specialized mini-packages for spike sorting, local regression, audio segmentation
and other tasks. It also includes a graphical user interface (GUI). The current version of the GUI contains a number of features specialised to the
analysis of electroencephalography (EEG) data. The eventual aim is to provide domain specific user interfaces (UIs) for each experimental modality,
along with corresponding data management tools. In particular, we expect
Chronux to grow to support analysis of time series data from most of the

1

CHAPTER 1. CHRONUX OVERVIEW

2

standard data acquisition modalities in use in neuroscience. We also expect
it to grow in the types of analyses it implements. Chronux is supported by
grant R01MH071744 from the NIH to Partha P. Mitra.

1.2

Installation and Setup

The Chronux website at http://chronux.org/ is the central location for
information about the current and all previous releases of Chronux. The
home page contains links to pages for downloads, people, recent news, tutorials, various files, documentation and our discussion forum. Most of the
code is written in the Matlab scripting language, with some exceptions as
compiled C code integrated using Matlab mex functions. Chronux has been
tested and runs under Matlab releases R13 to the current R2008a under the
Windows, Macintosh and Linux operating systems. Extensive online and
within-Matlab help is available. The code is available as a smaller zip file
(without data for testing) and a larger zip file that contains testing data.
To install Chronux, first unzip the zip archive into any location on your
computer. Then the the Matlab path must be set to include the Chronux
directory and all subdirectories (recursively) contained within. All Chronux
functions and help information are then available from the Matlab command
line.
Besides Matlab itself, Chronux requires the Matlab Signal Processing
Toolbox for proper operation. The specscope utility depends upon the Matlab Data Acquisition Toolbox as well. The Locfit and spikesort subpackages
utilize Matlab mex functions, which are pre-compiled and included for the
Windows and Linux platform. For the Mac platform recompilation of the
locfit and spikesort subpackages is currently necessary.
As an open source project released under the GNU Public License GPL
v2, we welcome development, code contributions, bug reports, and discussion from the community. To date, Chronux has been downloaded over 10000
times. Questions or comments about can be posted on our discussion forum
at http://chronux.org/forum/ (after account registration). Announcements are made through the google group chronux-announce.

CHAPTER 1. CHRONUX OVERVIEW

1.3

3

Documentation and Help

Documentation and help material for the Chronux package are provided in a
few different formats. The latest and most complete type of documentation is
the document you are currently reading. It contains this section on Chronux
usage in Matlab, and a cross-referenced comprehensive function reference at
the end. This document is expected to be the starting point for help for new
Chronux users.
Once Chronux is installed on your computer you will also be able to access
help material for each Chronux function from within the Matlab environment
using the Matlab help command. The help material for any Chronux function
can be accessed by typing help function-name. For example, to obtain
help for the mtspectrumc Chronux function, type help mtspectrumc at the
Matlab prompt. The output will typically contain the purpose and expected
usage of the function, with the format and allowed values for input arguments
explained in detail. The output (if any) of the function is also described. Note
that this material is only available through the Matlab command line using
the help command, and will not show up in searches in the GUI-based help
system in Matlab.
The Chronux function reference is also available online in hyperlinked
html format at http://chronux.org/documentation/. This reference material displays the purpose, usage, help text, source code and cross-referencing
information for all Chronux functions. It is created directly from the Chronux
source code using the Matlab utility m2html. For each Chronux subdirectory
a dependency graph is shown which helps users to understand the relationship between Chronux functions in a given subdirectory. This function reference is also included with the Chronux distribution in the documentation
subdirectory.
Finally, several tutorials for using Chronux are available at
http://chronux.org/tutorials/,
organized by the tutorial creator. Tutorials are provided which cover
signal processing and spectral analysis theory, Chronux usage for spectral
analysis and local regression. Other tutorials go into detail on spectral analysis and SVDs for neural time series. Another tutorial covers the practical
aspects of detrending neural data and line (or noise) removal. The final tutorial covers Image processing using SVDs and spectral analysis. Most of
these tutorials consist of a PDF or powerpoint presentation plus actual code
which you can execute as you read the presentation.

CHAPTER 1. CHRONUX OVERVIEW

1.4

4

Chronux Organization

On installing chronux, you should have a folder named chronux on your
computer. Since the main components of Chronux are the spectral analysis
toolbox, the local regression and likelihood toolbox and the spike-sorting
toolbox, these are subdirectories of the chronux folder. In addition, the
chronux folder also contains subdirectories for a specscope and wavebrowser
and Chronux GUI. Finally, it contains script called testscript in the test
directory that runs a test on each of the spectral analysis routines and a
subdirectory called tutorials that contains the tutorials mentioned above. As
the code and teaching material evolves, these directories will be get updated,
as will this manual.

Chapter 2
Spectral Analysis Toolbox
The spectral analysis toolbox is the heart of chronux and is perhaps its most
widely used component. It computes the spectrum of one or more time series
data as well as the coherence between two simultaneously measured time series. In addition, it computes multivariate measures such as the cross-spectral
matrix between multiple simultaneously measured time series. It also enables
computation of spectral derivatives. Finally, it allows the user to perform
harmonic analysis (identification and extraction of periodic components) on
time series data. All these computations are performed using the multi-taper
spectral estimation method. Where possible, Chronux provides confidence
intervals on estimated quantities using both asymptotic formulae based on
appropriate probabilistic models, as well as nonparametric bands based on
the Jackknife method. Chronux includes various statistical tests such as the
two-group tests for the spectrum and coherence and a test for nonstationarity
based on quadratic inverse theory.

2.1

Data Formats and Parameters

Chronux spectral analysis routines are supplied to operate on three basic
types of input data: continuous valued data and point process data supplied
as individual times or as binned counts. Accordingly, for each type of analysis there will generally be three separate functions available, depending upon
the input data type. For convenience, each such function is identified by an
appropriate suffix: c for continuous, pt for point times and pb for binned
point processes. For example, the multitaper spectrum function is available
5

CHAPTER 2. SPECTRAL ANALYSIS TOOLBOX

6

in the three forms: mtspectrumc, mtspectrumpt and mtspectrumpb. For
the functions where two data inputs of different format are used, two suffixes indicate the accepted data formats. For example, cohgramcpb is the
multitaper time-frequency coherence between continuous and binned point
data.
Continuous data is simply any data stream where the measurements are
provided at evenly sampled intervals. This type of data must be input to
Chronux routines in matrix form where the first dimension is time, and the
second dimension is channels or trials. Binned point process data is supplied
to the routines in the same matrix format as continuous data, but in this
case the values for each element are interpreted as counts. Point process data
supplied as times, on the other hand, must be input to Chronux routines as
a structure array of spike times (with field name ‘times’), with dimension of
channels or trials. The difference in format stems from the fact that each
channel or trial for spike time data will generally have a different length
because the number of spikes recorded will vary. This makes a standard
Matlab matrix inappropriate for the spike time data format. For singlechannel point time data an ordinary column vector can be used instead. Note
that point process data is usually derived from a continuous data stream in
hardware or software.
A number of frequently used and important spectral analysis parameters
to Chronux functions are passed for convenience in the Matlab structure
called params. The fields in the params structure are all optional, and are
named tapers, Fs, fpass, pad, err and trialave. We will discuss each of these
in detail in the following paragraphs.
• The tapers field of the params structure describes the scale and number
of tapers used in the multitaper calculation. This field is given as a
Matlab array [NW K], where N W is the time-bandwidth product and
K is the number of leading tapers to use. The default value here is [3
5]. You should generally set K to be 2N W − 1, as using more tapers
will include tapers with poor concentration in the specified frequency
bandwidth. The user may also specify this field as a 3 element array [W
T p]. In this case, W is interpreted as the bandwidth, T the duration
over which the tapers are to be computed and p is an integer such
that K = 2T W − p tapers are used. Note that T and W have to be
consistent with other quantities such as the field Fs.
• The Fs field of the params structure describes the sampling frequency

CHAPTER 2. SPECTRAL ANALYSIS TOOLBOX

7

of the input data, and controls the units used in the output. By default,
an Fs of 1 indicates a sampling frequency of 1 sample per second. Take
care that the value of Fs and the fpass and movingwin parameters
(described below) are given in consistent units.
• The fpass field of the params structure controls the range of frequencies
supplied in the output. This is given as a two element array with the
lower and upper bounds of frequency output. By default, the value of
fpass is [0 Fs/2]. These values, if supplied, must be given in units
consistent with the Fs parameter.
• The pad field of the params structure controls the amount of padding
used by the fast fourier transform (FFT) routine. This field is an
integer from -1 and up. The value -1 results in no padding, the value
0 results in padding the data length to the next power of 2, the value
1 goes a further power of 2, etc. Padding the data to a length of a
power of 2 improves the efficiency of the FFT algorithm, and increases
the number of frequency bins of the result. Although this procedure
does not affect the result calculation in any way, it does produce a
more finely interpolated output which may assist with visualization
and the precise identification of spectral lines. The default value for
this parameter is 0.
• The err field of the params structure controls the type of error bars
calculated (if any) for the output. It is supplied as a two element
matrix where the first element gives the type of error calculation and
the second element gives the p value used for the calculation. The
supported error calculation types are 0 for no error bar calculations, 1
for theoretical error bars and 2 for jackknife error bars. The default
value for the error type is 0 for no error bars. Note that requesting
error bars (where available) will result in an additional output result
from the function.
• The trialave field of the params structure governs whether or not trial or
channel averaging is performed on the quantity of interest. If trialave
is set to 0, no trial averaging is done, and the function will output
independent results for each trial or channel passed as input data. If
trialave is set to 1, the results passed to the user are averaged over
trials or channels. The default for trialave is 0, or no averaging. Note

CHAPTER 2. SPECTRAL ANALYSIS TOOLBOX

8

that setting trialave to 1 will result in a lower-dimensional output to
the user.
Another common parameter encountered in Chronux routines, although not
in the params structure, is the movingwin parameter. The movingwin parameter is used for the time-frequency version of the spectral analysis routines
where the quantity of interest is calculated as a function of time. Instead
of calculating a single spectrum of a dataset, the evolution of the spectrum
versus time can be determined by calculating the spectrum over many small
time windows. The result is frequently plotted as an image or a 3-dimensional
contour or surface plot. The movingwin parameter is given as a two element
array where the first element is the size of the moving window and the second
is the step size to advance the window. Both of these values must be given
in units consistent with params.Fs.

2.2

Examples

Space constraints preclude covering all of spectral analysis here, but the
functions generally have a uniform function calling signature. We illustrate
three canonical routines below.

2.2.1

mtspectrumc

As a first example, we show how to estimate the spectrum of a single trial
local field potential measured from macaque during a working memory task.
Figure 2.1 shows the spectrum estimated by the Chronux function mtspectrumc.
For comparison we also display the ordinary periodogram. In this case,
mtspectrumc was called with params.tapers=[5 9]. The
The Matlab calling signature of the mtspectrumc function is as follows:
[S,f,Serr] = mtspectrumc( data, params );
The first argument is the data matrix in the form of times * trials or
channels, while the second argument params is a Matlab structure defining
the sampling frequency1 , the time-bandwidth product used to compute the
1

The current version of Chronux assumes continuous valued data to be uniformly sampled

CHAPTER 2. SPECTRAL ANALYSIS TOOLBOX

9

Figure 2.1: Comparison of a periodogram (black) and multitaper estimate
(red or light) of a single trial local field potential measurement from macaque
during a working memory task. This estimate used 9 tapers.
tapers, and the amount of zero padding to use. It also contains flags controlling the averaging over trials and the error computation. In this example,
params.tapers was set to be [5 9], thus giving an estimate with a time
bandwidth product 5, using 9 tapers (For more details on this argument, see
below).
The three variables returned by mtspectrumc are, in order, the estimated
spectrum, the frequencies of estimation, and the confidence bands. The spectrum is in general two-dimensional, with the first dimension being the power
as a function of frequency and the second dimension being the trial or channel. The second dimension is 1 when the user requests a spectrum that
is averaged over the trials or channels. The confidence bands are provided
as a lower and upper confidence band at a p value set by the user. As
indicated by the last letter c in its name, the routine mtspectrumc is applicable to continuous valued data such as the local field potential or the
EEG. The corresponding routines for point processes are mtspectrumpt and
mtspectrumpb, applicable to point processes stored as a sequence of times

CHAPTER 2. SPECTRAL ANALYSIS TOOLBOX

10

and binned point processes, respectively. In addition to these routines, it
is also sometimes useful to compute the spectrum by breaking the data into
short segments and averaging the estimates over those segments. Such a computation is performed by the routines mtspectrumsegc, mtspectrumsegpb
and mtspectrumsegpt.
The rountines for point processes have one or two extra input arguments
compared to those for continous processes. One of these arguments is fscorr
which takes a value 0 if the user wants to compute Jackknife confidence bands
with a correction taking into account the number of spikes. This optional
argument is available for all point process rountines where Jackknife confidence bands are computed. Another argument, t is an input argument only
for point processes stored as spike times. This optional argument may contain the grid over which a point process fourier transform is to be computed.
This is useful because for a point process stored as times, simply knowing
the grid spacing is not enough to compute the tapers. One also needs to
know the width of the window. For example, given a sequence of spike times
0.2, 0.6, 0.8 seconds, the spectrum for the case when the trial was from 1
second long is different from that in the case where the trial was 2 seconds
long. This difference may be entered by specifying t.

2.2.2

mtspecgramc

The second example is a moving window version of mtspectrumc called
mtspecgramc. This function, and mtspecgrampt and mtspecgrampb, calculate the multitaper spectrum over a moving window with user adjustable
time width and step size. The calling signature of this function is:
[S,t,f,Serr] =
mtspecgramc( data, movingwin, params );
Note that the only differences from the mtspectrumc function signature
are in the function name, the additional movingwin argument and the addition of a return value t which contains the centers of the moving windows.
The movingwin argument is given as [winsize winstep] in units consistent
with the sampling frequency. The returned spectrum here is in general three
dimensional: times * frequency * channel or trial.
The variable params.tapers controls the computation of the tapers used
in the multitaper estimate. params.tapers is a two-dimensional vector whose

CHAPTER 2. SPECTRAL ANALYSIS TOOLBOX

11

Figure 2.2: The effect of changing the components of the time-bandwidth
product TW. a) T = 0.5s, W = 10Hz. b) T = 0.2s, W = 25Hz. Data from
macaque monkey performing a working memory task. Sharp enhancement
in high frequency power occurs during the memory period.
first element, T W , is the time-bandwidth product, where T is the duration
and W is the desired bandwidth. The second element of params.tapers is
the number of tapers to be used. For a given T W , the latter can be at most
2T W − 1. Higher order taper functions will not be sufficiently concentrated
in frequency and may lead to increased broadband bias if used. As discussed

CHAPTER 2. SPECTRAL ANALYSIS TOOLBOX

12

above, params.tapers may also be supplied as a 3 element vector [W T p].
In this case, there are no defaults and it is the user’s responsibility to ensure
consistency between these inputs and any other relevant ones. For example,
when computing a spectrogram, T has to equal the duration of the moving
window given by movingwin(1). Figure 2.2 shows the effect on the spectrogram of changing the time-bandwidth product. The data again consists of
local field potentials recorded from macaque during a working memory task.

2.2.3

coherencycpt

Figure 2.3: The spike-field coherence recorded from visual cortex of monkey,
showing significant differences between the attended and unattended conditions. In addition to the coherence in the two conditions, we also show the
95% confidence bands computed using the Jackknife. We thank Pascal Fries
for permission to use this figure.
Figure 2.3 [10] shows significant differences in the spike-field coherence
recorded from the primary visual cortex of monkeys during an attention
modulation task. The coherences were computed using coherencycpt. This
function is called with two timeseries as arguments: the continuous LFP data
and the corresponding spikes which are stored as event times. It returns
not only the magnitude and phase of the coherency, but the cross-spectrum
and individual spectra from which the coherence is computed. As with the
spectra, confidence intervals on the magnitude and phase of the coherency
may also be obtained. The calling signature here is

CHAPTER 2. SPECTRAL ANALYSIS TOOLBOX

13

[C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=
coherencycpt(data1,data2,params,fscorr,t)
confC contains a confidence level based on the assumption of zero population coherence, phistd contains the standard deviation of the phase estimate
and Cerr contains Jackknife estimates of the confidence bands around C if
they are asked for by the user. The output argument zerosp contains 1 for
trials in which there were no spikes and 0 otherwise.

Chapter 3
Locfit
Local regression and likelihood provide a powerful set of methods of fitting functions to data. Local regression refers to regression using moving
windows and local likelihood refers to a generalization of this to allow for
non-Gaussian errors. The Locfit package by Catherine Loader [6] is included
in Chronux. Locfit can be used for local regression, local likelihood estimation, local smoothing, density estimation, conditional hazard rate estimation,
classification and censored likelihood models. Locfit is written in C and is
available in Chronux through a mex interface to Matlab. From a neuroscience
user’s standpoint, the most important routines in Locfit are
• The rountine locfit.m computes the fits, whether they be for regression
or density estimation.
• The rountine lfband.m computes confidence bands.
• The routine lfplot.m generate plots of the fit.
In addtion, Locfit also has routines to compute cross-validation scores based
on the likelihood, the generalized cross-validation scores and the Akaike Information Criterion scores.

3.1

Data Format and Parameters

Locfit is a fairly extensive and involved package and full discussion of its
capabilities can be found in the book by Loader [6]. We restrict our discussion
to illustrating local regression based smoothing and local likelihood based
14

CHAPTER 3. LOCFIT

15

Figure 3.1: Schematic depiction of local regression. The data is a voltage
segment recorded from area LIP of macaque. A. In a window of duration
0.2 s centered on the point x, a second order polynomial is fitted to the
data using weighted least squares. The constant term of the polynomial fit
centered on at x is taken to be the estimate µ̂(x). We show local ploynomial
fits (degree two) in three windows as examples. As the window slides along
the data, a smooth fit is generated. B. Local regression fit generated by the
procedure described above.
rate estimation using Locfit. Finally, we illustrate the use of cross-validation
based assesment of the appropriate bandwidth.

3.1.1

Local Regression

Figure 3.1 shows a local regression based fit to a voltage segment recorded
from area LIP of macaque. The top panel shows third order polynomial fits
of the data in non-overlapping windows of 0.2 second duration. The bottom
panel shows the complete fit. In this case, the independent variable was time
and the dependent variable was the voltage and the calling sequence was
fit=locfit(t,V, ’h’,0.2)

CHAPTER 3. LOCFIT

16

The first and second argument is the dependent. Here, the name is ’h’, which
is the fixed bandwidth chosen to be equal to 0.2. Note that the units of h
have to be consistent with the units of the independent variable. Locfit may
also be used with a bandwidth that depends on the number of points in the
vicinity, as illustrated by the next example.

3.1.2

Local Likelihood

Figure 3.2 is an example of Locfit estimate of the rate given a sequence of
spike times. In this case, there is just one variable, the spike times and
Locfit was used to estimate the rate based on a local Poisson likelihood. The
local rate was modeled as a cubic polynomial. Also shown are the Locfit
computed 95% local confidence bands around the smoothed rate estimate.
For comparison a histogram is also shown. In this case, the calling sequence
was
fit=locfit(t,’deg’, 3, ’nn’,0.35)

Figure 3.2: A traditional binned histogram and a Locfit smoothed estimate
of the same data set. The Locfit estimate shown uses a nearest-neighbor
fraction of 35% when calculating the distribution.
Here, the names are ’deg’ which controls the polynomial degree (the default
is 2) and ’nn’ which denotes a nearest-neighbour bandwidth. With the name,
value pair ’nn’, 0.35, the local window is chosen to include 35% of the total

CHAPTER 3. LOCFIT

17

number of points. Thus, the window size decreases with increasing density
of points. Locfit also allows both variable and fixed bandwidths in the form
either of name,value pairs as above, or as a name,value pair involving a 2
element vector ’alpha’. In this case, the first argument of ’alpha’ is taken to
be the variable bandwidth and the second is taken to be the fixed bandwidth.
Note also that the larger of the two is used in the fit.

3.1.3

Model Selection

The essential idea behind model selection in Locfit is to use cross-validation.
One drops one point from the data in turn and estimates (by some measure)
how well the fit with the remaining points fits the dropped data point. Locfit
provides lilelihood based cross-validation (LCV) scores and an approximation
to it known as the generalized cross-validation (GCV) score which is easier to
compute. Figure 3.3 shows the GCV score for the data in Figure 3.1. Note
that it is conventional to plot the score vs. the degrees of freedom rather than
the bandwidth. The reason for this is that the meaning of the bandwidth
depends on the smoothing method and the degrees of freedom is a more
unambiguous measure. In our case, using about 12 − 15 degrees of freedom
seems reasonable. This corresponds to a bandwidth of around 200 − 250
samples. Figure 3.1 was computed with a bandwidth of 200 samples. The
calling sequence in this case was
gcvplot(alpha,t,V)
where alpha was a column vector of fixed bandwidths from 0.2 to 0.6. Variable bandwidths may also be specified in a second column of α.

CHAPTER 3. LOCFIT

18

Figure 3.3: GCV score vs. Degrees of Freedom for the data in Figure 3.1.

Chapter 4
Function Reference
4.1

CrossSpecMatc

Purpose:
Multi-taper cross-spectral matrix - another routine, allows for multiple trials
and channels
Synopsis:
function [Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMatc(data,win,params)

Comments:
Multi-taper cross-spectral matrix - another routine, allows for multiple trials and channels
Does not do confidence intervals. Also this routine always averages over trials - continuous process
Usage:
[Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMatc(data,win,params)
Input:
Note units have to be consistent. See chronux.m for more information.
data (in form samples x channels x trials)
win (duration of non-overlapping window)
params: structure with fields tapers, pad, Fs, fpass
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of

19

CHAPTER 4. FUNCTION REFERENCE
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional. Defaults to 0.
e.g. For N = 500, if PAD = 0, we pad the FFT
to 512 points; if PAD = 2, we pad the FFT
to 2048 points, etc.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
Output:
Sc (cross spectral matrix frequency x channels x channels)
Cmat Coherence matrix frequency x channels x channels
Ctot Total coherence: SV(1)^2/sum(SV^2) (frequency)
Cvec leading Eigenvector (frequency x channels)
Cent A different measure of total coherence: GM/AM of SV^2s
f (frequencies)

This function calls:
mtfftc (Section 4.55) Multi-taper fourier transform - continuous data

This function is called by:
none No functions call this function

20

CHAPTER 4. FUNCTION REFERENCE

4.2

21

CrossSpecMatpb

Synopsis:
function [Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMatpb(data,win,params)

Comments:

Multi-taper cross-spectral matrix - another routine, this one allows for multiple trials and channels
Does not do confidence intervals.
Also this routine always averages over trials - binned point process
Usage:
[Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMatpb(data,win,params)
Input:
Note units have to be consistent. See chronux.m for more information.
data (in form samples x channels x trials)
win (duration of non-overlapping window)
params: structure with fields tapers, pad, Fs, fpass
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
Output:
Sc (cross spectral matrix frequency x channels x channels)

CHAPTER 4. FUNCTION REFERENCE
Cmat Coherence matrix frequency x channels x channels
Ctot Total coherence: SV(1)^2/sum(SV^2) (frequency)
Cvec leading Eigenvector (frequency x channels)
Cent A different measure of total coherence: GM/AM of SV^2s
f (frequencies)

This function calls:
mtfftpb (Section 4.56) Multi-taper fourier transform - binned point process
data

This function is called by:
none No functions call this function

22

CHAPTER 4. FUNCTION REFERENCE

4.3

23

CrossSpecMatpt

Synopsis:
function [Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMatpt(data,win,T,params)

Comments:

Multi-taper cross-spectral matrix - another routine, this one allows for multiple trials and channels
but does not do confidence intervals. Also this routine always averages
over trials - point process as times
Usage:
[Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMatpt(data,win,T,params)
Input:
Note units have to be consistent. See chronux.m for more information.
data (as a struct array with dimensions channels x trials) - note
that times of measurement have to be consistent, we assume all
times are specified relative to the start time of the trials which
are taken to be zero.
win (duration of non-overlapping window)
trialduration (since it is not possible to infer trial duration
from spike times, this is an optional argument. If not specified
the routine uses the minimum and maximum spike time (across all
channels and trials) as the window of calculation.) optional
params: structure with fields tapers, pad, Fs, fpass
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT

CHAPTER 4. FUNCTION REFERENCE
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
Output:
Sc (cross spectral matrix frequency x channels x channels)
Cmat Coherence matrix frequency x channels x channels
Ctot Total coherence: SV(1)^2/sum(SV^2) (frequency)
Cvec leading Eigenvector (frequency x channels)
Cent A different measure of total coherence: GM/AM of SV^2s
f (frequencies)

This function calls:
extractdatapt (Section 4.38) Extract segements of spike times between t(1)
and t(2)
minmaxsptimes (Section 4.48) Find the minimum and maximum of the
spike times in each channel
mtfftpt (Section 4.57) Multi-taper fourier transform for point process given
as times

This function is called by:
none No functions call this function

24

CHAPTER 4. FUNCTION REFERENCE

4.4

binspikes

Purpose:
bin spikes at a specified frequency sampling i.e. sampling rate 1/sampling
Synopsis:
function [dN,t]=binspikes(data,Fs,t)
Comments:
bin spikes at a specified frequency sampling i.e. sampling rate 1/sampling
eg: 1ms accuracy use sampling = 1000
Usage: [dN,t]=binspikes(data,Fs,t)
Inputs:
data
(data as a structure array of spike times; or as a single
vector of spike times)
Fs
(binning frequency)
t
(the minimum and maximum times to be used to form the bins - [mint maxt]
- optional. Default use the spike times themselves to
determine the location of the bins.
Note: the times in data can be in any units. However, it is important
that all units are chosen consistently. So, if spike times are in secs,
Fs and t (if present) have to be in Hz and secs respectively. If spike
times are in number of samples, Fs has to be 1, and t has to be in number
of samples.
Outputs:
dN
(output binned spike counts as a matrix defined on bins starting with the
earliest spike across all channels and ending with the latest spike)
t
(lower limit of each bin)

This function calls:
none This function calls no functions

This function is called by:
none No functions call this function

25

CHAPTER 4. FUNCTION REFERENCE

4.5

change row to column

Purpose:
Helper routine to transform 1d arrays into column vectors that are needed
Synopsis:
function data=change row to column(data)
Comments:
Helper routine to transform 1d arrays into column vectors that are needed
by other routines in Chronux
Usage: data=change_row_to_column(data)
Inputs:
data -- required. If data is a matrix, it is assumed that it is of the
form samples x channels/trials and it is returned without change. If it
is a vector, it is transformed to a column vector. If it is a struct
array of dimension 1, it is again returned as a column vector. If it is a
struct array with multiple dimensions, it is returned without change
Note that the routine only looks at the first field of a struct array.
Ouputs:
data (in the form samples x channels/trials)

This function calls:
none This function calls no functions

This function is called by:
none No functions call this function

26

CHAPTER 4. FUNCTION REFERENCE

4.6

check consistency

Purpose:
Helper routine to check consistency of data dimensions
Synopsis:
function [N,C]=check consistency(data1,data2,sp)
Comments:
Helper routine to check consistency of data dimensions
Usage: [N,C]=check_consistency(data1,data2,sp)
Inputs:
data1 - first dataset
data2 - second dataset
sp - optional argument to be input as 1 when one of the two data sets is
spikes times stored as a 1d array.
Outputs:
Dimensions of the datasets - data1 or data2 (note that
routine stops with an error message if dimensions don’t match - [N,C]
N left empty for structure arrays

This function calls:
none This function calls no functions

This function is called by:
none No functions call this function

27

CHAPTER 4. FUNCTION REFERENCE

4.7

chronux

Purpose:
This library performs time-frequency analysis (mostly using the
Synopsis:
function chronux
Comments:
This library performs time-frequency analysis (mostly using the
multi-taper spectral estimation method) of univariate and multivariate
data, both for continuous processes such as LFP/EEG and for point
processes such as spike times. Point process can either be stored as
times or as a binned process of counts. The routines in this library
are named differently for the three cases. For calculations
that can be performed for each of the three data types, we use suffixes
c, pb, or pt to refer to continuous, point process binned counts, or
point process times. For example, the spectrum calculation is performed
mtspectrumc for continuous processes, mtspectrumpb for a binned point
process, and mtspectrumpt for a point process consisting of times. There
are also routines for calculating hybrid quantities involving one continuous
and one point process. These are suffixed in a similar manner. For
example, coherencycpb calculates the coherency between a binned point process
and a continuous process.
Certain variables are used repeatedly in this library.
DATA
data in most cases can be univariate or multivariate, and either point process,
or continuous.
Continuous data: Continuous data is assumed to be a matrix with
dimensions samples x channels/trials.
Point Process: A single time series of spike times can be in the form of
a column vector.
Multichannel/trial spike time data is not amenable to this
storage format, since there are generally different
number of spikes in each channel/trial. Instead,
multichannel/trial spike data is stored in a structure
array. A structure is a matlab data object with various
fields. These fields contain the elements
e.g. The command data=struct(’times’,[]); creates an empty
structure with field ’times’. Similarly, the command
data=struct(’times’,[1 2 3]); creates the structure with
the field ’times’ containing integers 1, 2, and 3.
We can also have a structure array (or an array of structures)
defined for example, by
data(1)=struct(’times’,rand(1,100)); and
data(2)=struct(’times’,rand(1,200));

28

CHAPTER 4. FUNCTION REFERENCE
This is a 2 dimensional structure array where the
first field is a 100 dimensional random vector, and
the second field is a 200 dimensional random vector.
This format allows storage of multichannel point
process times in a single variable data.
The above holds for point processes stored as times.
If instead, the point processes are binned, then one
can use a matrix to represent them

Summary: data - array of continuous data with dimensions time x channels
structural array of spike times with dimensions
equal to the number of channels
1d array of spike times as a column vector
array of binned spike counts with dimensions time x channels
PARAMETERS:
These are various parameters used in the spectral calculations. Since
these parameters are used by most routines in Chronux, they are stored in
a single structure params. The fields of params are
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5

pad:

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.

Fs:sampling frequency.optional (default 1)

fpass: frequencies in an fft calculation can range from 0 to Fs/2 where
Fs is the sampling frequency. Sometimes it may be useful to
compute fourier transforms (and resulting quantities like the

29

CHAPTER 4. FUNCTION REFERENCE
spectrum over a smaller range of frequencies). This is specified
by fpass, which can be in the form [fmin fmax] where fmin >=0 and
fmax<=Fs/2. optional (default [0 Fs/2])
err=[errtype p] calculates theoretical error bars (confidence levels)
when errtype=1 and jackknife error bars when errchk=2. In each case, the
error is calculated at a p value specified by p. optional (default 0)
trialave: trialave controls whether or not to average over channels/trials for
multichannel/trial analyses. trialave=0 (default) implies no trial
averaging, trialave=1 implies that the quantity of interest is averaged
over channels/trials. optional (default 0)
Other parameters are discussed in individual routines as and when they
are used.

This function calls:
none This function calls no functions

This function is called by:
none No functions call this function

30

CHAPTER 4. FUNCTION REFERENCE

4.8

coherencyc

Purpose:
Multi-taper coherency,cross-spectrum and individual spectra - continuous
process
Synopsis:
function [C,phi,S12,S1,S2,f,confC,phistd,Cerr]=coherencyc(data1,data2,params)

Comments:
Multi-taper coherency,cross-spectrum and individual spectra - continuous process
Usage:
[C,phi,S12,S1,S2,f,confC,phistd,Cerr]=coherencyc(data1,data2,params)
Input:
Note units have to be consistent. See chronux.m for more information.
data1 (in form samples x trials) -- required
data2 (in form samples x trials) -- required
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.

31

CHAPTER 4. FUNCTION REFERENCE

32

trialave (average over trials when 1, don’t average when 0) - optional. Default 0
Output:
C (magnitude of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
phi (phase of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S12 (cross spectrum - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S1 (spectrum 1 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S2 (spectrum 2 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
f (frequencies)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi.
Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
bands for phi - only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

This function calls:
mtfftc (Section 4.55) Multi-taper fourier transform - continuous data

This function is called by:
coherencysegc (Section 4.14) Multi-taper coherency, cross-spectrum and
individual spectra with segmenting - continuous process
cohgramc (Section 4.20) Multi-taper time-frequency coherence,cross-spectrum
and individual spectra - continuous processes

CHAPTER 4. FUNCTION REFERENCE

33

coherencyc unequal length trials

4.9

Purpose:
This routine computes the average multi-taper coherence for a given set of
unequal length segments. It is
Synopsis:
function [Cmn,Phimn,Smn,Smm,f,ConfC,PhiStd,Cerr] = coherencyc unequal length trials(
data, movingwin, params, sMarkers )
Comments:
This routine computes the average multi-taper coherence for a given set of unequal length segments. It is
based on modifications to the Chronux routines. The segments are continuously structured in the
data matrix, with the segment boundaries given by markers. Below,
movingwin is used in a non-overlaping way to partition each segment into
various windows. Th coherence is evaluated for each window, and then the
window coherence estimates averaged. Further averaging is conducted by
repeating the process for each segment.
Inputs:
data = data( samples, channels )- here segments must be stacked
as explained in the email
movingwin = [window winstep] i.e length of moving
window and step size. Note that units here have
to be consistent with units of Fs. If Fs=1 (ie normalized)
then [window winstep]should be in samples, or else if Fs is
unnormalized then they should be in time (secs).
sMarkers = N x 2 array of segment start & stop marks. sMarkers(n, 1) = start
sample index; sMarkers(n,2) = stop sample index for the nth segment
params = see Chronux help on mtspecgramc
Output:
Cmn
Phimn
Smn
Smm
f
ConfC
PhiStd
Cerr

magnitude of coherency - frequencies x iChPairs
phase of coherency - frequencies x iChPairs
cross spectrum - frequencies x iChPairs
spectrum m - frequencies x channels
frequencies x 1
1 x iChPairs; confidence level for Cmn at 1-p % - only for err(1)>=1
frequency x iChPairs; error bars for phimn - only for err(1)>=1
2 x frequency x iChPairs; Jackknife error bars for Cmn - use only for Jackknife - err(1)=2

Here iChPairs = indices corresponding to the off-diagonal terms of the
lower half matrix. iChPairs = 1 : nChannels*(nChannels-1)/2. So,
iChPairs=1,2,3,4,...correspond to C(2,1), C(3,1), C(3,2), C(4,1), etc.
The mapping can be obtained as follows:
C(i,j) = Cmn(:,k) where k = j + (1/2)*(i-1)*(i-2)
The above also applies to phimn, Smn

CHAPTER 4. FUNCTION REFERENCE

34

Note:
segment length >= NW/2 where NW = half bandwidth parameter (see dpss). So the power spectrum will
be computed only for those segments whose length > NW/2. For that reason, the routine returns the
indices for segments for which the spectra is computed. This check is
done here since pSpecgramAvg calls it.

This function calls:
mtfftc (Section 4.55) Multi-taper fourier transform - continuous data

This function is called by:
none No functions call this function

CHAPTER 4. FUNCTION REFERENCE

4.10

35

coherencycpb

Purpose:
Multi-taper coherency,cross-spectrum and individual spectra - continuous
and binned point process data
Synopsis:
function [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencycpb(data1,data2,params,fscorr)

Comments:
Multi-taper coherency,cross-spectrum and individual spectra - continuous and binned point process data
Usage:
[C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencycpb(data1,data2,params,fscorr)
Inputs:
data1 (continuous data in form samples x trials) -- required
data2 (binned spike data in form samples x trials) -- required
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.

CHAPTER 4. FUNCTION REFERENCE

36

trialave (average over trials when 1, don’t average when 0) - optional. Default 0
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or 1
(use finite size corrections) - optional (available only for spikes). Defaults 0.
Outputs:
C (magnitude of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
phi (phase of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S12 (cross spectrum - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S1 (spectrum 1 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S2 (spectrum 2 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
f (frequencies)
zerosp (1 for trials where no spikes were found, 0 otherwise)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
bands for phi - only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

This function calls:
none This function calls no functions

This function is called by:
coherencysegcpb (Section 4.15) Multi-taper coherency,cross-spectrum and
individual spectra with segmenting
cohgramcpb (Section 4.21) Multi-taper time-frequency coherence,cross-spectrum
and individual spectra

CHAPTER 4. FUNCTION REFERENCE

4.11

37

coherencycpt

Purpose:
Multi-taper coherency,cross-spectrum and individual spectra -continuous data
and point process as times

Synopsis:
function [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencycpt(data1,data2,params,fscorr,t

Comments:
Multi-taper coherency,cross-spectrum and individual spectra -continuous data and point process as times
Usage:
[C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencycpt(data1,data2,params,fscorr,t)
Input:
data1
(continuous data in time x trials form) -- required
data2
(structure array of spike times with dimension trials;
also accepts 1d array of spike times) -- required
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars

CHAPTER 4. FUNCTION REFERENCE

38

[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over trials when 1, don’t average when 0) - optional. Default 0
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
t
(time grid over which the tapers are to be calculated:
this argument is useful when calling the spectrum
calculation routine from a moving window spectrogram
calculation routine). If left empty, the spike times
are used to define the grid.
Output:
C (magnitude of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
phi (phase of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S12 (cross spectrum - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S1 (spectrum 1 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S2 (spectrum 2 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
f (frequencies)
zerosp (1 for trials where no spikes were found, 0 otherwise)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
bands for phi - only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

This function calls:
none This function calls no functions

This function is called by:
coherencysegcpt (Section 4.16) Multi-taper coherency,cross-spectrum and
individual spectra computed by segmenting
cohgramcpt (Section 4.22) Multi-taper time-frequency coherence,cross-spectrum
and individual spectra

CHAPTER 4. FUNCTION REFERENCE

4.12

39

coherencypb

Purpose:
Multi-taper coherency,cross-spectrum and individual spectra - binned point
process
Synopsis:
function [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencypb(data1,data2,params,fscorr)

Comments:
Multi-taper coherency,cross-spectrum and individual spectra - binned point process
Usage:
[C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencypb(data1,data2,params,fscorr)
Input:
data1 (in form samples x trials) -- required
data2 (in form samples x trials) -- required
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.

CHAPTER 4. FUNCTION REFERENCE

40

trialave (average over trials when 1, don’t average when 0) - optional. Default 0
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
Output:
C (magnitude of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
phi (phase of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S12 (cross spectrum - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S1 (spectrum 1 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S2 (spectrum 2 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
f (frequencies)
zerosp (1 for trials in either channel where spikes were absent, zero otherwise)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - jackknife/theoretical standard deviation for phi. Note that
phi + 2 phistd and phi -2 phistd will give 95% confidence bands
for phi - only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

This function calls:
mtfftpb (Section 4.56) Multi-taper fourier transform - binned point process
data

This function is called by:
coherencysegpb (Section 4.17) Multi-taper coherency,cross-spectrum and
individual spectra computed by segmenting
cohgrampb (Section 4.23) Multi-taper time-frequency coherence,cross-spectrum
and individual spectra - two binned point processes

CHAPTER 4. FUNCTION REFERENCE

4.13

41

coherencypt

Purpose:
Multi-taper coherency - point process times

Synopsis:
function [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencypt(data1,data2,params,fscorr,t)

Comments:
Multi-taper coherency - point process times
Usage:

[C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencypt(data1,data2,params,fscorr,t)
Input:
data1 (structure array of spike times with dimension trials; also accepts 1d array of spike times) -- r
data2 (structure array of spike times with dimension trials; also accepts 1d array of spike times) -- r
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over trials when 1, don’t average when 0) - optional. Default 0

CHAPTER 4. FUNCTION REFERENCE
fscorr

t

42

(finite size corrections, 0 (don’t use finite size corrections)
or 1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
(time grid over which the tapers are to be calculated:
this argument is useful when calling the spectrum
calculation routine from a moving window spectrogram
calculation routine). If left empty, the spike times
are used to define the grid.

Output:
C (magnitude of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
phi (phase of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S12 (cross spectrum - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S1 (spectrum 1 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S2 (spectrum 2 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
f (frequencies)
zerosp (1 for trials where no spikes were found, 0 otherwise)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
bands for phi - only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

This function calls:
minmaxsptimes (Section 4.48) Find the minimum and maximum of the
spike times in each channel
mtfftpt (Section 4.57) Multi-taper fourier transform for point process given
as times

This function is called by:
coherencysegpt (Section 4.18) Multi-taper coherency computed by segmenting two univariate point processes into chunks
cohgrampt (Section 4.24) Multi-taper time-frequency coherence - two point
processes given as times

CHAPTER 4. FUNCTION REFERENCE

4.14

coherencysegc

Purpose:
Multi-taper coherency, cross-spectrum and individual spectra with segmenting - continuous process
Synopsis:
function [C,phi,S12,S1,S2,f,confC,phistd,Cerr]=coherencysegc(data1,data2,win,params)

Comments:
Multi-taper coherency, cross-spectrum and individual spectra with segmenting - continuous process
computed by segmenting two univariate time series into chunks
Usage:
[C,phi,S12,S1,S2,f,confC,phistd,Cerr]=coherencysegc(data1,data2,win,params)
Input:
Note units have to be consistent. See chronux.m for more information.
data1 (column vector) -- required
data2 (column vector) -- required
win
(length of segments) - required
params: structure with fields tapers, pad, Fs, fpass, err
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2

43

CHAPTER 4. FUNCTION REFERENCE
err

44

(error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.

Output:
C (magnitude of coherency - frequencies x segments if segave=0; dimension frequencies if segave=1)
phi (phase of coherency - frequencies x segments if segave=0; dimension frequencies if segave=1)
S12 (cross spectrum - frequencies x segments if segave=0; dimension frequencies if segave=1)
S1 (spectrum 1 - frequencies x segments if segave=0; dimension frequencies if segave=1)
S2 (spectrum 2 - frequencies x segments if segave=0; dimension frequencies if segave=1)
f (frequencies)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
bands for phi - only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

This function calls:
coherencyc (Section 4.8) Multi-taper coherency,cross-spectrum and individual spectra - continuous process
createdatamatc (Section 4.30) Helper function to create an event triggered
matrix from univariate

This function is called by:
none No functions call this function

CHAPTER 4. FUNCTION REFERENCE

4.15

45

coherencysegcpb

Purpose:
Multi-taper coherency,cross-spectrum and individual spectra with segmenting

Synopsis:
function [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencysegcpb(data1,data2,win,params,s

Comments:
Multi-taper coherency,cross-spectrum and individual spectra with segmenting
computed by segmenting two univariate time series into chunks - continuous and binned point process
Usage:
[C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencysegcpb(data1,data2,win,params,segave,fscorr)
Input:
Note units have to be consistent. See chronux.m for more information.
data1 (column vector, continuous data) -- required
data2 (column vector, binned point process data) -- required
win
(length of segments) - required
params: structure with fields tapers, pad, Fs, fpass, err
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2

CHAPTER 4. FUNCTION REFERENCE
err

46

(error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
segave (average over segments for 1, don’t average for 0)
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
Output:
C (magnitude of coherency - frequencies x segments if segave=0; dimension frequencies if segave=1)
phi (phase of coherency - frequencies x segments if segave=0; dimension frequencies if segave=1)
S12 (cross spectrum - frequencies x segments if segave=0; dimension frequencies if segave=1)
S1 (spectrum 1 - frequencies x segments if segave=0; dimension frequencies if segave=1)
S2 (spectrum 2 - frequencies x segments if segave=0; dimension frequencies if segave=1)
f (frequencies)
zerosp (1 for trials where no spikes were found, 0 otherwise)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
bands for phi - only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

This function calls:
coherencycpb (Section 4.10) Multi-taper coherency,cross-spectrum and individual spectra - continuous and binned point process data

This function is called by:
none No functions call this function

CHAPTER 4. FUNCTION REFERENCE

4.16

47

coherencysegcpt

Purpose:
Multi-taper coherency,cross-spectrum and individual spectra computed by
segmenting

Synopsis:
function [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencysegcpt(data1,data2,win,params,s

Comments:
Multi-taper coherency,cross-spectrum and individual spectra computed by segmenting
two univariate time series into chunks - continuous and point process stored as times
Usage:
[C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencysegcpt(data1,data2,win,params,segave,fscorr)
Input:
Note units have to be consistent. See chronux.m for more information.
data1 (column vector, continuous data) -- required
data2 (1d structure array of spike times; also accepts 1d array of spike times) -- required
params: structure with fields tapers, pad, Fs, fpass, err
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars

CHAPTER 4. FUNCTION REFERENCE

48

[0 p] or 0 - no error bars) - optional. Default 0.
segave (average over segments for 1, don’t average for 0)- optional. Default 1
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
Output:
C (magnitude of coherency - frequencies x segments if segave=0; dimension frequencies if segave=1)
phi (phase of coherency - frequencies x segments if segave=0; dimension frequencies if segave=1)
S12 (cross spectrum - frequencies x segments if segave=0; dimension frequencies if segave=1)
S1 (spectrum 1 - frequencies x segments if segave=0; dimension frequencies if segave=1)
S2 (spectrum 2 - frequencies x segments if segave=0; dimension frequencies if segave=1)
f (frequencies)
zerosp (1 for trials where no spikes were found, 0 otherwise)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
bands for phi - only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

This function calls:
coherencycpt (Section 4.11) Multi-taper coherency,cross-spectrum and individual spectra -continuous data and point process as times

This function is called by:
none No functions call this function

CHAPTER 4. FUNCTION REFERENCE

4.17

49

coherencysegpb

Purpose:
Multi-taper coherency,cross-spectrum and individual spectra computed by
segmenting

Synopsis:
function [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencysegpb(data1,data2,win,params,se

Comments:
Multi-taper coherency,cross-spectrum and individual spectra computed by segmenting
two univariate binned point processes into chunks
Usage:
[C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencysegpb(data1,data2,win,params,segave,fscorr)
Input:
Note units have to be consistent. See chronux.m for more information.
data1 (column vector, binned point process data) -- required
data2 (column vector, binned point process data) -- required
win
(length of segments) - required
params: structure with fields tapers, pad, Fs, fpass, err
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2

CHAPTER 4. FUNCTION REFERENCE
err

50

(error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
segave (average over segments for 1, don’t average for 0)
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
Output:
C (magnitude of coherency - frequencies x segments if segave=0; dimension frequencies if segave=1)
phi (phase of coherency - frequencies x segments if segave=0; dimension frequencies if segave=1)
S12 (cross spectrum - frequencies x segments if segave=0; dimension frequencies if segave=1)
S1 (spectrum 1 - frequencies x segments if segave=0; dimension frequencies if segave=1)
S2 (spectrum 2 - frequencies x segments if segave=0; dimension
frequencies if segave=1)
f (frequencies)
zerosp (1 for segments where no spikes were found, 0 otherwise)
confC (confidence level for C at 1-p %)
phistd - jackknife/theoretical standard deviation for phi - Note that
phi + 2 phistd and phi -2 phistd will give 95% confidence bands for phi only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife)

This function calls:
coherencypb (Section 4.12) Multi-taper coherency,cross-spectrum and individual spectra - binned point process
createdatamatpb (Section 4.31)

This function is called by:
none No functions call this function

CHAPTER 4. FUNCTION REFERENCE

4.18

51

coherencysegpt

Purpose:
Multi-taper coherency computed by segmenting two univariate point processes into chunks

Synopsis:
function [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencysegpt(data1,data2,win,params,se

Comments:
Multi-taper coherency computed by segmenting two univariate point processes into chunks
Usage:
[C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencysegpt(data1,data2,win,params,segave,fscorr)
Input:
Note units have to be consistent. See chronux.m for more information.
data1 (1d structure array of spike times; also accepts 1d array of spike times) -- required
data2 (1d structure array of spike times; also accepts 1d array of spike times) -- required
win
(length of segments) - required
params: structure with fields tapers, pad, Fs, fpass, err
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars

CHAPTER 4. FUNCTION REFERENCE

52

[0 p] or 0 - no error bars) - optional. Default 0.
segave - optional 0 for don’t average over segments, 1 for average - default
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
Output:
C (magnitude of coherency - frequencies x segments if segave=0; dimension frequencies if segave=1)
phi (phase of coherency - frequencies x segments if segave=0; dimension frequencies if segave=1)
S12 (cross spectrum - frequencies x segments if segave=0; dimension frequencies if segave=1)
S1 (spectrum 1 - frequencies x segments if segave=0; dimension frequencies if segave=1)
S2 (spectrum 2 - frequencies x segments if segave=0; dimension frequencies if segave=1)
f (frequencies)
zerosp (1 for segments where no spikes were found, 0 otherwise)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
bands for phi - only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

This function calls:
coherencypt (Section 4.13) Multi-taper coherency - point process times
createdatamatpt (Section 4.32) Helper function to create an event triggered matrix from a single
minmaxsptimes (Section 4.48) Find the minimum and maximum of the
spike times in each channel

This function is called by:
none No functions call this function

CHAPTER 4. FUNCTION REFERENCE

4.19

coherr

Purpose:
Function to compute lower and upper confidence intervals on the coherency
Synopsis:
function [confC,phistd,Cerr]=coherr(C,J1,J2,err,trialave,numsp1,numsp2)

Comments:
Function to compute lower and upper confidence intervals on the coherency
given the tapered fourier transforms, errchk, trialave.
Usage: [confC,phistd,Cerr]=coherr(C,J1,J2,err,trialave,numsp1,numsp2)
Inputs:
C
- coherence
J1,J2 - tapered fourier transforms
err - [errtype p] (errtype=1 - asymptotic estimates; errchk=2 - Jackknife estimates;
p - p value for error estimates)
trialave - 0: no averaging over trials/channels
1 : perform trial averaging
numsp1
- number of spikes for data1. supply only if finite size corrections are required
numsp2
- number of spikes for data2. supply only if finite size corrections are required
Outputs:
confC - confidence level for C - only for err(1)>=1
phistd - theoretical or jackknife standard deviation for phi for err(1)=1 and err(1)=2
respectively. returns zero if coherence is 1
Cerr - Jacknife error bars for C - only for err(1)=2

This function calls:
none This function calls no functions

This function is called by:
cohmathelper (Section 4.25) Helper function called by coherency matrix
computations.

53

CHAPTER 4. FUNCTION REFERENCE

4.20

54

cohgramc

Purpose:
Multi-taper time-frequency coherence,cross-spectrum and individual spectra
- continuous processes
Synopsis:
function [C,phi,S12,S1,S2,t,f,confC,phistd,Cerr]=cohgramc(data1,data2,movingwin,params)

Comments:
Multi-taper time-frequency coherence,cross-spectrum and individual spectra - continuous processes
Usage:
[C,phi,S12,S1,S2,t,f,confC,phistd,Cerr]=cohgramc(data1,data2,movingwin,params)
Input:
Note units have to be consistent. Thus, if movingwin is in seconds, Fs
has to be in Hz. see chronux.m for more information.
data1 (in form samples x trials) -- required
data2 (in form samples x trials) -- required
movingwin (in the form [window winstep] -- required
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Note that T has to be equal to movingwin(1).
pad

Fs

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
(sampling frequency) - optional. Default 1.

CHAPTER 4. FUNCTION REFERENCE
fpass

(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over trials when 1, don’t average when 0) - optional. Default 0
Output:
C (magnitude of coherency time x frequencies x trials for trialave=0;
time x frequency for trialave=1)
phi (phase of coherency time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
S12 (cross spectrum - time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
S1 (spectrum 1 - time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
S2 (spectrum 2 - time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
t (time)
f (frequencies)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
bands for phi - only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

This function calls:
coherencyc (Section 4.8) Multi-taper coherency,cross-spectrum and individual spectra - continuous process

This function is called by:
none No functions call this function

55

CHAPTER 4. FUNCTION REFERENCE

4.21

56

cohgramcpb

Purpose:
Multi-taper time-frequency coherence,cross-spectrum and individual spectra

Synopsis:
function [C,phi,S12,S1,S2,t,f,zerosp,confC,phistd,Cerr]=cohgramcpb(data1,data2,movingwin,param

Comments:
Multi-taper time-frequency coherence,cross-spectrum and individual spectra
continuous process and binned point process
Usage:
[C,phi,S12,S1,S2,t,f,zerosp,confC,phistd,Cerr]=cohgramcpb(data1,data2,movingwin,params,fscorr)
Input:
Note units have to be consistent. Thus, if movingwin is in seconds, Fs
has to be in Hz. see chronux.m for more information.
data1 (continuous data in form samples x trials) -- required
data2 (binned point process data in form samples x trials) -- required
movingwin (in the form [window winstep] -- required
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Note that T has to be equal to movingwin(1).
pad

Fs

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
(sampling frequency) - optional. Default 1.

CHAPTER 4. FUNCTION REFERENCE
fpass

57

(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over trials when 1, don’t average when 0) - optional. Default 0
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
Output:
C (magnitude of coherency time x frequencies x trials for trialave=0;
time x frequency for trialave=1)
phi (phase of coherency time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
S12 (cross spectrum - time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
S1 (spectrum 1 - time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
S2 (spectrum 2 - time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
t (time)
f (frequencies)
zerosp (1 for windows and trials where no spikes were found, 0 otherwise: dimensions time x trials)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
bands for phi - only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

This function calls:
coherencycpb (Section 4.10) Multi-taper coherency,cross-spectrum and individual spectra - continuous and binned point process data

This function is called by:
none No functions call this function

CHAPTER 4. FUNCTION REFERENCE

4.22

58

cohgramcpt

Purpose:
Multi-taper time-frequency coherence,cross-spectrum and individual spectra

Synopsis:
function [C,phi,S12,S1,S2,t,f,zerosp,confC,phistd,Cerr]=cohgramcpt(data1,data2,movingwin,param

Comments:
Multi-taper time-frequency coherence,cross-spectrum and individual spectra
continuous process and point process times
Usage:
[C,phi,S12,S1,S2,t,f,zerosp,confC,phistd,Cerr]=cohgramcpt(data1,data2,movingwin,params,fscorr)
Input:
Note units have to be consistent. Thus, if movingwin is in seconds, Fs
has to be in Hz. see chronux.m for more information.
data1 (continuous data in form samples x trials) -- required
data2 (structure array of spike times with dimension trials;
also accepts 1d array of spike times) -- required
movingwin (in the form [window winstep] -- required
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Note that T has to be equal to movingwin(1).
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.

CHAPTER 4. FUNCTION REFERENCE
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over trials when 1, don’t average when 0) - optional. Default 0
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
Output:
C (magnitude of coherency time x frequencies x trials for trialave=0;
time x frequency for trialave=1)
phi (phase of coherency time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
S12 (cross spectrum - time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
S1 (spectrum 1 - time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
S2 (spectrum 2 - time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
t (time)
f (frequencies)
zerosp (1 for windows where no spikes were found, 0 otherwise;
dimensions time x trials if no trial averaging)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
bands for phi - only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

This function calls:
coherencycpt (Section 4.11) Multi-taper coherency,cross-spectrum and individual spectra -continuous data and point process as times

This function is called by:
none No functions call this function

59

CHAPTER 4. FUNCTION REFERENCE

4.23

60

cohgrampb

Purpose:
Multi-taper time-frequency coherence,cross-spectrum and individual spectra
- two binned point processes

Synopsis:
function [C,phi,S12,S1,S2,t,f,zerosp,confC,phistd,Cerr]=cohgrampb(data1,data2,movingwin,params

Comments:
Multi-taper time-frequency coherence,cross-spectrum and individual spectra - two binned point processes
Usage:
[C,phi,S12,S1,S2,t,f,zerosp,confC,phistd,Cerr]=cohgrampb(data1,data2,movingwin,params,fscorr)
Input:
Note units have to be consistent. Thus, if movingwin is in seconds, Fs
has to be in Hz. see chronux.m for more information.
data1 (binned point process data in form samples x trials) -- required
data2 (binned point process data in form samples x trials) -- required
movingwin (in the form [window winstep] -- required
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Note that T has to be equal to movingwin(1).
pad

Fs

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
(sampling frequency) - optional. Default 1.

CHAPTER 4. FUNCTION REFERENCE
fpass

(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over trials when 1, don’t average when 0) optional. Default 0
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
Output:
C (magnitude of coherency time x frequencies x trials for trialave=0;
time x frequency for trialave=1)
phi (phase of coherency time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
S12 (cross spectrum - time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
S1 (spectrum 1 - time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
S2 (spectrum 2 - time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
t (time)
f (frequencies)
zerosp (1 for windows and trials where spikes were absent (in either channel),zero otherwise)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - jackknife/theoretical standard deviation for phi - Note that
phi + 2 phistd and phi -2 phistd will give 95% confidence bands for phi
- only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

This function calls:
coherencypb (Section 4.12) Multi-taper coherency,cross-spectrum and individual spectra - binned point process

This function is called by:
none No functions call this function

61

CHAPTER 4. FUNCTION REFERENCE

4.24

62

cohgrampt

Purpose:
Multi-taper time-frequency coherence - two point processes given as times

Synopsis:
function [C,phi,S12,S1,S2,t,f,zerosp,confC,phistd,Cerr]=cohgrampt(data1,data2,movingwin,params

Comments:
Multi-taper time-frequency coherence - two point processes given as times
Usage:
[C,phi,S12,S1,S2,t,f,zerosp,confC,phistd,Cerr]=cohgrampt(data1,data2,movingwin,params,fscorr)
Input:
Note units have to be consistent. Thus, if movingwin is in seconds, Fs
has to be in Hz. see chronux.m for more information.

data1 (structure array of spike times with dimension trials; also accepts 1d array of spike times) -- r
data2 (structure array of spike times with dimension trials; also accepts 1d array of spike times) -- r
movingwin (in the form [window winstep] -- required
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Note that T has to be equal to movingwin(1).
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form

CHAPTER 4. FUNCTION REFERENCE
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over trials when 1, don’t average when 0) - optional. Default 0
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
Output:
C (magnitude of coherency time x frequencies x trials for trialave=0;
time x frequency for trialave=1)
phi (phase of coherency time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
S12 (cross spectrum - time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
S1 (spectrum 1 - time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
S2 (spectrum 2 - time x frequencies x trials for no trial averaging;
time x frequency for trialave=1)
t (time)
f (frequencies)
zerosp (1 for windows and trials where spikes were absent (in either channel),zero otherwise)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
bands for phi - only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

This function calls:
coherencypt (Section 4.13) Multi-taper coherency - point process times
extractdatapt (Section 4.38) Extract segements of spike times between t(1)
and t(2)
minmaxsptimes (Section 4.48) Find the minimum and maximum of the
spike times in each channel

This function is called by:
none No functions call this function

63

CHAPTER 4. FUNCTION REFERENCE

4.25

cohmathelper

Purpose:
Helper function called by coherency matrix computations.
Synopsis:
function [C,phi,S12,confC,phierr,Cerr]=cohmathelper(J,err,Nsp)
Comments:
Helper function called by coherency matrix computations.
Usage: [C,phi,S12,confC,phierr,Cerr]=cohmathelper(J,err,Nsp)
Inputs:
J
: Fourier transforms of data
err : [0 p] or 0 for no errors; [1 p] for theoretical confidence level,
[2 p] for Jackknife (p - p value)
Nsp : pass the number of spikes in each channel if finite size corrections are desired
Outputs:
C
:
phi :
S12 :
confC

Cerr

coherence
phase of coherency
cross spectral matrix
: confidence level for coherency - only for err(1)>=1
phierr - standard deviation for phi (note that the routine gives phierr as phierr(1,...)
and phierr(2,...) in order to incorporate Jackknife (eventually).
Currently phierr(1,...)=phierr(2,...). Note that phi + 2 phierr(1,...) and phi -2
phierr(2,...) will give 95% confidence bands for phi - only for err(1)>=1
: error bars for coherency (only for Jackknife estimates)-only for err(1)=2

This function calls:
coherr (Section 4.19) Function to compute lower and upper confidence intervals on the coherency

This function is called by:
none No functions call this function

64

CHAPTER 4. FUNCTION REFERENCE

4.26

cohmatrixc

Purpose:
Multi-taper coherency,cross-spectral matrix - continuous process
Synopsis:
function [C,phi,S12,f,confC,phistd,Cerr]=cohmatrixc(data,params)

Comments:
Multi-taper coherency,cross-spectral matrix - continuous process
Usage:
[C,phi,S12,f,confC,phistd,Cerr]=cohmatrixc(data,params)
Input:
Note units have to be consistent. See chronux.m for more information.
data (in form samples x channels) -- required
params: structure with fields tapers, pad, Fs, fpass, err
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
Output:

65

CHAPTER 4. FUNCTION REFERENCE
C (magnitude of coherency frequency x channels x channels)
phi (phase of coherency frequency x channels x channels)
S12 (cross-spectral matrix frequency x channels x channels)
f (frequencies)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
bands for phi - only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

This function calls:
mtfftc (Section 4.55) Multi-taper fourier transform - continuous data

This function is called by:
none No functions call this function

66

CHAPTER 4. FUNCTION REFERENCE

4.27

cohmatrixpb

Purpose:
Multi-taper coherency matrix - binned point process
Synopsis:
function [C,phi,S12,f,zerosp,confC,phistd,Cerr]=cohmatrixpb(data,params,fscorr)

Comments:
Multi-taper coherency matrix - binned point process
Usage:
[C,phi,S12,f,zerosp,confC,phistd,Cerr]=cohmatrixpb(data,params,fscorr)
Input:
data (in form samples x channels) -- required
params: structure with fields tapers, pad, Fs, fpass, err
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional

67

CHAPTER 4. FUNCTION REFERENCE
(available only for spikes). Defaults 0.
Output:
C (magnitude of coherency frequency x channels x channels)
phi (phase of coherency frequency x channels x channels)
S12 (cross-spectral matrix frequency x channels x channels)
f (frequencies)
zerosp (1 for channels where no spikes were found, zero otherwise)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - jackknife/theoretical standard deviation for phi - Note that
phi + 2 phistd and phi -2 phistd will give 95% confidence bands for phi
- only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

This function calls:
mtfftpb (Section 4.56) Multi-taper fourier transform - binned point process
data

This function is called by:
none No functions call this function

68

CHAPTER 4. FUNCTION REFERENCE

4.28

cohmatrixpt

Purpose:
Multi-taper coherency matrix - point process times
Synopsis:
function [C,phi,S12,f,zerosp,confC,phistd,Cerr]=cohmatrixpt(data,params,fscorr)

Comments:
Multi-taper coherency matrix - point process times
Usage:
[C,phi,S12,f,zerosp,confC,phistd,Cerr]=cohmatrixpt(data,params,fscorr)
Input:
data
(structure array of spike times with dimension channels) - required
params: structure with fields tapers, pad, Fs, fpass, err
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional

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CHAPTER 4. FUNCTION REFERENCE
(available only for spikes). Defaults 0.
Output:
C (magnitude of coherency frequency x channels x channels)
phi (phase of coherency frequency x channels x channels)
S12 (cross-spectral matrix frequency x channels x channels)
f (frequencies)
zerosp (1 for channels where no spikes were found, zero otherwise)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
bands for phi - only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

This function calls:
minmaxsptimes (Section 4.48) Find the minimum and maximum of the
spike times in each channel
mtfftpt (Section 4.57) Multi-taper fourier transform for point process given
as times

This function is called by:
none No functions call this function

70

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4.29

countsig

Purpose:
Give the program two spike data sets and one
Synopsis:
function[H,P,M1,M2,N1,N2] = countsig(data1,data2,T1,T2,parametric,p,quiet)

Comments:
Give the program two spike data sets and one
or two time intervals and it will decide if
the counts are significantly different.
this is either with a non-parametric method
or with a sqrt transformation followed by a
t-test
Usage: [H,P,M1,M2,N1,N2] = countsig(data1,data2,T1,T2,parametric,p,quiet)
Input:
Note that all times have to be consistent. If data
is in seconds, so must be sig and t. If data is in
samples, so must sig and t. The default is seconds.
data1
data2
T1
T2
parametric

p
quiet

-

structure array of spike times (required)
structure array of spike times (required)
time interval (default all)
time interval (default T1)
0 = non-parametric (Wilcoxon)
1 = ttest on sqrt of counts
2 = Poisson assumption
(default = 0)
- significance level (0.05)
- 1 = no display 0 = display

Output:
H
P
M1
M2
N1
N2

-

1 if different 0 if not
prob of result if same
mean count for data1
mean count for data2
counts for data1
counts for data2

This function calls:
padNaN (Section 4.77) Creates a padded data matrix from input structural
array of spike times
This function is called by:

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none No functions call this function

72

CHAPTER 4. FUNCTION REFERENCE

4.30

createdatamatc

Purpose:
Helper function to create an event triggered matrix from univariate
Synopsis:
function data=createdatamatc(data,E,Fs,win)
Comments:
Helper function to create an event triggered matrix from univariate
continuous data
Usage: data=createdatamatc(data,E,Fs,win)
Inputs:
data
(input time series as a column vector) - required
E
(events to use as triggers) - required
Fs
(sampling frequency of data) - required
win
(window around triggers to use data matrix -[winl winr]) - required
e.g [1 1] uses a window starting 1 * Fs samples before E and
ending 1*Fs samples after E.
Note that E, Fs, and win must have consistent units
Outputs:
data

(event triggered data)

This function calls:
none This function calls no functions

This function is called by:
coherencysegc (Section 4.14) Multi-taper coherency, cross-spectrum and
individual spectra with segmenting - continuous process
mtspecgramtrigc (Section 4.62) Multi-taper event triggered time-frequency
spectrum - continuous process
mtspectrum of spectrumc (Section 4.65) Multi-taper segmented, second
spectrum (spectrum of the log spectrum) for a continuous process
mtspectrumsegc (Section 4.70) Multi-taper segmented spectrum for a univariate continuous process
mtspectrumtrigc (Section 4.73) Multi-taper event triggered time-frequency
spectrum - continuous process

73

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4.31

createdatamatpb

Synopsis:
function data=createdatamatpb(data,E,Fs,win)
Comments:
Helper function to create an event triggered matrix from a single
channel of data.
Usage: data=createdatamatpb(data,E,Fs,win)
Inputs:
data
(input time series as a single vector) - required
E
(events to use as triggers) - required
Fs
(sampling frequency of data) - required
win
(window around triggers to use data matrix -[winl winr]) - required
e.g [1 1] uses a window starting 1 sec before E and
ending 1 sec after E if E is in secs
Note that E, Fs, and win must have consistent units
Outputs:
data

(event triggered data)

This function calls:
none This function calls no functions

This function is called by:
coherencysegpb (Section 4.17) Multi-taper coherency,cross-spectrum and
individual spectra computed by segmenting
mtspecgramtrigpb (Section 4.63) Multi-taper event triggered time-frequency
spectrum - binned point process
mtspectrumsegpb (Section 4.71) Multi-taper segmented spectrum for a
univariate binned point process
mtspectrumtrigpb (Section 4.74) Multi-taper event triggered time-frequency
spectrum - binned point process

74

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4.32

createdatamatpt

Purpose:
Helper function to create an event triggered matrix from a single
Synopsis:
function data=createdatamatpt(data,E,win)
Comments:
Helper function to create an event triggered matrix from a single
channel of spike times.
Usage: data=createdatamatpt(data,E,win)
Inputs:
data
(input spike times as a structural array or as a column vector) - required
E
(events to use as triggers) - required
win
(window around triggers to use data matrix -[winl winr]) - required
e.g [1 1] uses a window starting 1 sec before E and
ending 1 sec after E if E and data are in secs.
Note that E, win and data must have consistent units
Outputs:
data
(event triggered data as a structural array - times are stored
relative to the E-winl

This function calls:
none This function calls no functions

This function is called by:
coherencysegpt (Section 4.18) Multi-taper coherency computed by segmenting two univariate point processes into chunks
mtspecgramtrigpt (Section 4.64) Multi-taper event triggered time-frequency
spectrum - point process times
mtspectrumsegpt (Section 4.72) Multi-taper segmented spectrum for a
univariate binned point process
mtspectrumtrigpt (Section 4.75) Multi-taper time-frequency spectrum point process times

75

CHAPTER 4. FUNCTION REFERENCE

4.33

den jack

Purpose:
Function to compute smooth estimates of the mean of x using locfit,
Synopsis:
function [m,ll,ul,llj,ulj]=den jack(X,family,varargin)
Comments:
Function to compute smooth estimates of the mean of x using locfit,
the corresponding confidence intervals, and jackknife estimates of
the confidence intervals
Usage: [m,ll,ul,llj,ulj]=den_jack(x)
Inputs:
X: data in the form samples x trials
family: ’density’ or ’reg’ for regression
If the family is density, the entire input matrix X is considered
as data. If the family is regression then the first column of X is
taken to be the independent variable and the remaining columns are
regressed on this variable (for example, the first column may be
the centers of the bins for binned spike count data)
varargin is the set of arguments used by locfit to perform the smoothing
Outputs:
m : smoothed estimate of the mean
ll : estimate of the lower confidence level
ul : estimate of the upper confidence level
llj : jackknife estimate of the lower confidence level (+2\sigma
where sigma is the jackknife variance)
llu : jackknife estimate of the upper confidence level (-2\sigma
where sigma is the jackknife variance)

This function calls:
jackknife (Section 4.45) Compute jackknife estimates of the mean and standard deviation of input data x

This function is called by:
none No functions call this function

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4.34

dpsschk

Purpose:
Helper function to calculate tapers and, if precalculated tapers are supplied,
Synopsis:
function [tapers,eigs]=dpsschk(tapers,N,Fs)
Comments:
Helper function to calculate tapers and, if precalculated tapers are supplied,
to check that they (the precalculated tapers) the same length in time as
the time series being studied. The length of the time series is specified
as the second input argument N. Thus if precalculated tapers have
dimensions [N1 K], we require that N1=N.
Usage: tapers=dpsschk(tapers,N,Fs)
Inputs:
tapers
(tapers in the form of:
(i) precalculated tapers or,
(ii) [NW K] - time-bandwidth product, number of tapers)
N
Fs

Outputs:
tapers
eigs

(number of samples)
(sampling frequency - this is required for nomalization of
tapers: we need tapers to be such
that integral of the square of each taper equals 1
dpss computes tapers such that the
SUM of squares equals 1 - so we need
to multiply the dpss computed tapers
by sqrt(Fs) to get the right
normalization)
(calculated or precalculated tapers)
(eigenvalues)

This function calls:
none This function calls no functions

This function is called by:
none No functions call this function

77

CHAPTER 4. FUNCTION REFERENCE

4.35

evoked

Purpose:
Function to calculate the evoked response given continuous data in the
Synopsis:
function [V,t,Err] = evoked(data,Fs,win,width,plt,err)
Comments:
Function to calculate the evoked response given continuous data in the
form time x channels
Usage [V,t,Err] = evoked(data,Fs,win,width,plt,err)
Inputs
Note that all times can be in arbitrary units. But the units have to be
consistent. So, if win is in secs, width is in secs and Fs has to be Hz.
If win is in samples, so is width and Fs=1.
data(times, channels/trials or a single vector)
(required)
Fs sampling frequency
(required)
win
subsection of data to be used. Default all available data
width (s) of smoothing kernel. Default 50 samples
plt plot ’n’ for no plot, otherwise plot color. Default blue colored lines.
err = 0/1. Default 1=calculate bootstrap errorbars.
Outputs
V = evoked potential
t = times of evaluation
Err = bootstrap statdard deviation

This function calls:
locsmooth (Section 4.47) Running line fit (using local linear regression) 1d only, continuous

This function is called by:
none No functions call this function

78

CHAPTER 4. FUNCTION REFERENCE

4.36

extractdatac

Purpose:
Extract segements of continuous data between t(1) and t(2)
Synopsis:
function data=extractdatac(data,Fs,t)
Comments:
Extract segements of continuous data between t(1) and t(2)
Usage: data=extractdatac(data,Fs,t)
Input:
data: continous data in the form samples x channels or a single vector
Fs: sampling frequency
t
: time as a 2d vector [t(1) t(2)]
Note that sampling frequency and t have to be in consistent units
Output:
data: data between t(1) and t(2)

This function calls:
none This function calls no functions

This function is called by:
none No functions call this function

79

CHAPTER 4. FUNCTION REFERENCE

4.37

extractdatapb

Purpose:
Extract segements of binned point process data between t(1) and t(2)
Synopsis:
function data=extractdatapb(data,Fs,t)
Comments:
Extract segements of binned point process data between t(1) and t(2)
Usage: data=extractdatapb(data,Fs,t)
Input:
data: binned point process data in the form samples x channels or single
vector
Fs: sampling frequency
t
: time as a 2d vector [t(1) t(2)]
Note that sampling frequency and t have to be in consistent units
Output:
data: data between t(1) and t(2)

This function calls:
none This function calls no functions

This function is called by:
none No functions call this function

80

CHAPTER 4. FUNCTION REFERENCE

4.38

extractdatapt

Purpose:
Extract segements of spike times between t(1) and t(2)
Synopsis:
function data=extractdatapt(data,t,offset)
Comments:
Extract segements of spike times between t(1) and t(2)
Usage: data=extractdatapt(data,t,offset)
Input:
data: structural array of spike times for each channel/trial or a single
array of spike times
t
: time as a 2d vector [t(1) t(2)]
offset: 0/1 - if 1, store the spike times relative to start of window i.e. t(1)
if 0, don’t reset the times. Default 0.
Note that all times can be in arbitrary units. But the units have to be
consistent. So, if E is in secs, win, t have to be in secs, and Fs has to
be Hz. If E is in samples, so are win and t, and Fs=1. In case of spike
times, the units have to be consistent with the units of data as well.
Output:
data: spike times between t(1) and t(2)

This function calls:
none This function calls no functions

This function is called by:
CrossSpecMatpt (Section 4.3)
cohgrampt (Section 4.24) Multi-taper time-frequency coherence - two point
processes given as times
mtdspecgrampt (Section 4.51) Multi-taper derivative time-frequency spectrum - point process times
mtspecgrampt (Section 4.61) Multi-taper time-frequency spectrum - point
process times

81

CHAPTER 4. FUNCTION REFERENCE

4.39

findpeaks

Purpose:
Helper function to find peaks in a given continuous valued time series x
Synopsis:
function xmax=findpeaks(data,threshold)
Comments:
Helper function to find peaks in a given continuous valued time series x
Usage: xmax=findpeaks(data,threshold)
Input:
data
(data in time x channels/trials form or a single vector)
threshold (if specified returns locations of peaks at which data exceeds threshold) - optional
Output:
xmax
(locations of local maxima of data in a structure array of dimensions channels/trials)

This function calls:
none This function calls no functions

This function is called by:
fitlinesc (Section 4.40) fits significant sine waves to data (continuous data).

82

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4.40

fitlinesc

Purpose:
fits significant sine waves to data (continuous data).
Synopsis:
function [datafit,Amps,freqs,Fval,sig]=fitlinesc(data,params,p,plt,f0)

Comments:
fits significant sine waves to data (continuous data).
Usage: [datafit,Amps,freqs,Fval,sig]=fitlinesc(data,params,p,plt,f0)
Inputs:
Note that units of Fs, fpass have to be consistent.
data
(data in [N,C] i.e. time x channels/trials or a single
vector) - required.
params
structure containing parameters - params has the
following fields: tapers, Fs, fpass, pad
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Fs

(sampling frequency) -- optional. Defaults to 1.
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
(P-value to calculate error bars for) - optional.
Defaults to 0.05/N where N is data length.
(y/n for plot and no plot respectively) - plots the

fpass

pad

p
plt

83

CHAPTER 4. FUNCTION REFERENCE
Fratio at all frequencies if y
f0
frequencies at which you want to remove the
lines - if unspecified the program
will compute the significant lines

Outputs:
datafit
Amps
freqs
Fval
sig

(linear superposition of fitted sine waves)
(amplitudes at significant frequencies)
(significant frequencies)
(Fstatistic at all frequencies)
(significance level for F distribution p value of p)

This function calls:
findpeaks (Section 4.39) Helper function to find peaks in a given continuous
valued time series x
ftestc (Section 4.41) computes the F-statistic for sine wave in locally-white
noise (continuous data).

This function is called by:
rmlinesc (Section 4.85) removes significant sine waves from data (continuous data).
rmlinesmovingwinc (Section 4.86) fits significant sine waves to data (continuous data) using overlapping windows.

84

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4.41

ftestc

Purpose:
computes the F-statistic for sine wave in locally-white noise (continuous
data).
Synopsis:
function [Fval,A,f,sig,sd] = ftestc(data,params,p,plt)
Comments:
computes the F-statistic for sine wave in locally-white noise (continuous data).
[Fval,A,f,sig,sd] = ftestc(data,params,p,plt)
Inputs:
data
(data in [N,C] i.e. time x channels/trials or a single
vector) - required.
params
structure containing parameters - params has the
following fields: tapers, Fs, fpass, pad
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Fs
fpass

pad

p

plt

(sampling frequency) -- optional. Defaults to 1.
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
(P-value to calculate error bars for) - optional.
Defaults to 0.05/N where N is the number of samples which
corresponds to a false detect probability of approximately 0.05.
(y/n for plot and no plot respectively)

85

CHAPTER 4. FUNCTION REFERENCE

Outputs:
Fval
A
f
sig
sd

(F-statistic in frequency x channels/trials form)
(Line amplitude for X in frequency x channels/trials form)
(frequencies of evaluation)
(F distribution (1-p)% confidence level)
(standard deviation of the amplitude C)

This function calls:
mtfftc (Section 4.55) Multi-taper fourier transform - continuous data
mtspectrumc (Section 4.66) Multi-taper spectrum - continuous process

This function is called by:
fitlinesc (Section 4.40) fits significant sine waves to data (continuous data).

86

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4.42

getfgrid

Purpose:
Helper function that gets the frequency grid associated with a given fft based
computation
Synopsis:
function [f,findx]=getfgrid(Fs,nfft,fpass)
Comments:
Helper function that gets the frequency grid associated with a given fft based computation
Called by spectral estimation routines to generate the frequency axes
Usage: [f,findx]=getfgrid(Fs,nfft,fpass)
Inputs:
Fs
(sampling frequency associated with the data)-required
nfft
(number of points in fft)-required
fpass
(band of frequencies at which the fft is being calculated [fmin fmax] in Hz)-required
Outputs:
f
(frequencies)
findx
(index of the frequencies in the full frequency grid). e.g.: If
Fs=1000, and nfft=1048, an fft calculation generates 512 frequencies
between 0 and 500 (i.e. Fs/2) Hz. Now if fpass=[0 100], findx will
contain the indices in the frequency grid corresponding to frequencies <
100 Hz. In the case fpass=[0 500], findx=[1 512].

This function calls:
none This function calls no functions

This function is called by:
none No functions call this function

87

CHAPTER 4. FUNCTION REFERENCE

4.43

getparams

Purpose:
Helper function to convert structure params to variables used by the
Synopsis:
function [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params)

Comments:
Helper function to convert structure params to variables used by the
various routines - also performs checks to ensure that parameters are
defined; returns default values if they are not defined.
Usage: [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params)
Inputs:
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over trials when 1, don’t average when 0) - optional. Default 0
Outputs:

88

CHAPTER 4. FUNCTION REFERENCE
The fields listed above as well as the struct params. The fields are used
by some routines and the struct is used by others. Though returning both
involves overhead, it is a safer, simpler thing to do.

This function calls:
none This function calls no functions

This function is called by:
none No functions call this function

89

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4.44

isi

Purpose:
Calculate the inter-spike-interval histogram
Synopsis:
function[N,B,E] = isi(data,T,err,Nbins,plt)
Comments:
Calculate the inter-spike-interval histogram
Usage: [N,B,E] = isi(data,T,err,Nbins,plt)
Input:
Note that all times have to be consistent.
data
T
err

- structure array of spike times (required)
- time interval of interest (default all)
- 0 for no error bars, 1 for jackknife errors

Nbins

- number of bins in the isi

Output:
N
B
E

- count in bins
- bin centres
- errorbar (this is 2 sig deviation
calculated using a jackknife over trials)

This function calls:
padNaN (Section 4.77) Creates a padded data matrix from input structural
array of spike times

This function is called by:
none No functions call this function

90

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4.45

jackknife

Purpose:
Compute jackknife estimates of the mean and standard deviation of input
data x
Synopsis:
function [m,jsd]=jackknife(x)
Comments:
Compute jackknife estimates of the mean and standard deviation of input data x
Usage: [m,jsd]=jackknife(x)
Inputs:
x : data in the form samples x trials
Outputs:
m : estimate of the mean (across trials)
jsd: jackknife estimate of the standard deviation (across trials)

This function calls:
none This function calls no functions

This function is called by:
den jack (Section 4.33) Function to compute smooth estimates of the mean
of x using locfit,

91

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4.46

locdetrend

Purpose:
Remove running line fit (using local linear regression)-continuous
Synopsis:
function data=locdetrend(data,Fs,movingwin)
Comments:
Remove running line fit (using local linear regression)-continuous
processes
Usage: data=locdetrend(data,Fs,movingwin)
Inputs:
Note that units of Fs, movinwin have to be consistent.
data
(data as a matrix times x channels or a single vector)
Fs
(sampling frequency) - optional. Default 1
movingwin
(length of moving window, and stepsize) [window winstep] - optional.
Default. window=full length of data (global detrend).
winstep=window -- global detrend
Output:
data:

(locally detrended data)

This function calls:
runline (Section 4.87) Running line fit (local linear regression)

This function is called by:
none No functions call this function

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CHAPTER 4. FUNCTION REFERENCE

4.47

locsmooth

Purpose:
Running line fit (using local linear regression) - 1d only, continuous
Synopsis:
function data=locsmooth(data,Fs,Tw,Ts)
Comments:
Running line fit (using local linear regression) - 1d only, continuous
processes
Usage: data=locsmooth(data,Fs,Tw,Ts)
Inputs:
Note that units of Fs, movinwin have to be consistent.
data (single vector)
Fs
(sampling frequency) - optional. Default 1
Tw
(length of moving window) - optional. Default. full length of data (global detrend)
Ts
(step size) - optional. Default Tw/2.
Output:
data
(locally smoothed data).

This function calls:
runline (Section 4.87) Running line fit (local linear regression)

This function is called by:
evoked (Section 4.35) Function to calculate the evoked response given continuous data in the

93

CHAPTER 4. FUNCTION REFERENCE

4.48

minmaxsptimes

Purpose:
Find the minimum and maximum of the spike times in each channel
Synopsis:
function [mintime, maxtime]=minmaxsptimes(data)
Comments:
Find the minimum and maximum of the spike times in each channel
Usage: [mintime, maxtime]=minmaxsptimes(data)
Input:
data (spike times as a structural array of multiple dimensions e.g. channels; channels x trials;
can also accept a 1d matrix of spike times)
Output:
mintime
(minimum of the spike time across channels)
maxtime
(maximum of the spike time across channels)

This function calls:
none This function calls no functions

This function is called by:
CrossSpecMatpt (Section 4.3)
coherencypt (Section 4.13) Multi-taper coherency - point process times
coherencysegpt (Section 4.18) Multi-taper coherency computed by segmenting two univariate point processes into chunks
cohgrampt (Section 4.24) Multi-taper time-frequency coherence - two point
processes given as times
cohmatrixpt (Section 4.28) Multi-taper coherency matrix - point process
times
mtdspecgrampt (Section 4.51) Multi-taper derivative time-frequency spectrum - point process times
mtdspectrumpt (Section 4.54) Multi-taper spectral derivative - point process times
mtspecgrampt (Section 4.61) Multi-taper time-frequency spectrum - point
process times
mtspectrumpt (Section 4.69) Multi-taper spectrum - point process times

94

CHAPTER 4. FUNCTION REFERENCE
mtspectrumsegpt (Section 4.72) Multi-taper segmented spectrum for a
univariate binned point process

95

CHAPTER 4. FUNCTION REFERENCE

4.49

mtdspecgramc

Purpose:
Multi-taper derivative of the time-frequency spectrum - continuous process
Synopsis:
function [dS,t,f]=mtdspecgramc(data,movingwin,phi,params)
Comments:
Multi-taper derivative of the time-frequency spectrum - continuous process
Usage:
[dS,t,f]=mtdspecgramc(data,movingwin,phi,params)
Input:
Note that all times can be in arbitrary units. But the units have to be
consistent. So, if E is in secs, win, t have to be in secs, and Fs has to
be Hz. If E is in samples, so are win and t, and Fs=1. In case of spike
times, the units have to be consistent with the units of data as well.
data
movingwin

(in form samples x channels/trials or a single vector) -- required
(in the form [window winstep] i.e length of moving
window and step size.
Note that units here have
to be consistent with
units of Fs - required
phi
(angle for evaluation of derivative) -- required
e.g. phi=[0,pi/2] giving the time and frequency
derivatives
params: structure with fields tapers, pad, Fs, fpass, trialave
-optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Note that T has to be equal to movingwin(1).
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).

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97

-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
trialave - (average over trials/channels when 1, don’t average when 0) - optional. Default 0
Output:
dS
t
f

(spectral derivative in form phi x time x frequency x channels/trials if trialave=0;
in form phi x time x frequency if trialave=1)
(times)
(frequencies)

This function calls:
mtdspectrumc (Section 4.52) Multi-taper frequency derivative of the spectrum - continuous process

This function is called by:
none No functions call this function

CHAPTER 4. FUNCTION REFERENCE

4.50

mtdspecgrampb

Purpose:
Multi-taper derivatives of time-frequency spectrum - binned point process
Synopsis:
function [dS,t,f]=mtdspecgrampb(data,movingwin,phi,params)
Comments:
Multi-taper derivatives of time-frequency spectrum - binned point process
Usage:
[dS,t,f]=mtdspecgrampb(data,movingwin,phi,params)
Input:
Note that all times can be in arbitrary units. But the units have to be
consistent. So, if E is in secs, win, t have to be in secs, and Fs has to
be Hz. If E is in samples, so are win and t, and Fs=1. In case of spike
times, the units have to be consistent with the units of data as well.
data
(in form samples x channels/trials or a single vector) -- required
movingwin
(in the form [window winstep] i.e length of moving
window and step size.
Note that units here have
to be consistent with
units of Fs
phi
(angle for evaluation of derivative) -- required.
e.g. phi=[0,pi/2] giving the time and frequency
derivatives
params: structure with fields tapers, pad, Fs, fpass,trialave
-optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Note that T has to be equal to movingwin(1).
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding

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CHAPTER 4. FUNCTION REFERENCE
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and
Fs/2
trialave (average over trials when 1, don’t average when 0) optional. Default 0
Output:
dS
t
f

(spectral derivative in form phi x time x frequency x channels/trials if trialave=0;
phi x time x frequency if trialave=1)
(times)
(frequencies)

This function calls:
mtdspectrumpb (Section 4.53) Multi-taper spectral derivative - binned
point process

This function is called by:
none No functions call this function

99

CHAPTER 4. FUNCTION REFERENCE

4.51

mtdspecgrampt

Purpose:
Multi-taper derivative time-frequency spectrum - point process times
Synopsis:
function [dS,t,f]=mtdspecgrampt(data,movingwin,phi,params)
Comments:
Multi-taper derivative time-frequency spectrum - point process times
Usage:
[dS,t,f]=mtdspecgrampt(data,movingwin,phi,params)
Input:
Note that all times can be in arbitrary units. But the units have to be
consistent. So, if E is in secs, win, t have to be in secs, and Fs has to
be Hz. If E is in samples, so are win and t, and Fs=1. In case of spike
times, the units have to be consistent with the units of data as well.
data
(structure array of spike times with dimension channels/trials;
also accepts 1d array of spike times) -- required
movingwin
(in the form [window winstep] i.e length of moving
window and step size.
Note that units here have
to be consistent with
units of Fs
phi
(angle for evaluation of derivative) -- required.
e.g. phi=[0,pi/2] giving the time and frequency
derivatives
params: structure with fields tapers, pad, Fs, fpass, trialave
-optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Note that T has to be equal to movingwin(1).
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).

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CHAPTER 4. FUNCTION REFERENCE
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and
Fs/2
trialave (average over trials when 1, don’t average when 0) optional. Default 0
Output:
dS
t
f

(spectral derivative in form phi x time x frequency x channels/trials if trialave=0;
in form phi x time x frequency if trialave=1)
(times)
(frequencies)

This function calls:
extractdatapt (Section 4.38) Extract segements of spike times between t(1)
and t(2)
minmaxsptimes (Section 4.48) Find the minimum and maximum of the
spike times in each channel
mtdspectrumpt (Section 4.54) Multi-taper spectral derivative - point process times

This function is called by:
none No functions call this function

101

CHAPTER 4. FUNCTION REFERENCE

4.52

mtdspectrumc

Purpose:
Multi-taper frequency derivative of the spectrum - continuous process
Synopsis:
function [dS,f]=mtdspectrumc(data,phi,params)
Comments:
Multi-taper frequency derivative of the spectrum - continuous process
Usage:
[dS,f]=mtdspectrumc(data,phi,params)
Input:
Note that all times can be in arbitrary units. But the units have to be
consistent. So, if E is in secs, win, t have to be in secs, and Fs has to
be Hz. If E is in samples, so are win and t, and Fs=1. In case of spike
times, the units have to be consistent with the units of data as well.
data
(in form samples x channels/trials or a single vector) -- required
phi
(angle for evaluation of derivative) -- required.
e.g. phi=[0,pi/2] gives the time and frequency derivatives
params: structure with fields tapers, pad, Fs, fpass, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.

102

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103

Default all frequencies between 0 and Fs/2
trialave (average over trials/channels when 1, don’t average when 0) - optional. Default 0
Output:
dS
f

(spectral derivative in form phi x frequency x channels/trials if trialave=0 or
in form phi x frequency if trialave=1)
(frequencies)

This function calls:
mtfftc (Section 4.55) Multi-taper fourier transform - continuous data

This function is called by:
mtdspecgramc (Section 4.49) Multi-taper derivative of the time-frequency
spectrum - continuous process

CHAPTER 4. FUNCTION REFERENCE

4.53

mtdspectrumpb

Purpose:
Multi-taper spectral derivative - binned point process
Synopsis:
function [dS,f]=mtdspectrumpb(data,phi,params)
Comments:
Multi-taper spectral derivative - binned point process
Usage:
[dS,f]=mtdspectrumpb(data,phi,params)
Input:
Note that all times can be in arbitrary units. But the units have to be
consistent. So, if E is in secs, win, t have to be in secs, and Fs has to
be Hz. If E is in samples, so are win and t, and Fs=1. In case of spike
times, the units have to be consistent with the units of data as well.
data (in form samples x channels/trials or single vector) -- required
tapers (precalculated tapers from dpss, or in the form [NW K] e.g [3 5]) -- optional.
If not specified, use [NW K]=[3 5]
phi
(angle for evaluation of derivative) -- required.
e.g. phi=[0,pi/2] giving the time and frequency
derivatives
params: structure with fields tapers, pad, Fs, fpass, trialave
-optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.

104

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105

Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and
Fs/2
trialave (average over trials when 1, don’t average when 0) optional. Default 0
Output:
dS
f

(derivative of the spectrum in form phi x frequency x channels/trials if trialave=0;
in the form phi x frequency if trialave=1)
(frequencies)

This function calls:
mtfftpb (Section 4.56) Multi-taper fourier transform - binned point process
data

This function is called by:
mtdspecgrampb (Section 4.50) Multi-taper derivatives of time-frequency
spectrum - binned point process

CHAPTER 4. FUNCTION REFERENCE

4.54

mtdspectrumpt

Purpose:
Multi-taper spectral derivative - point process times
Synopsis:
function [dS,f]=mtdspectrumpt(data,phi,params,t)
Comments:
Multi-taper spectral derivative - point process times
Usage:
[dS,f]=mtdspectrumpt(data,phi,params,t)
Input:
Note that all times can be in arbitrary units. But the units have to be
consistent. So, if E is in secs, win, t have to be in secs, and Fs has to
be Hz. If E is in samples, so are win and t, and Fs=1. In case of spike
times, the units have to be consistent with the units of data as well.
data
(structure array of spike times with dimension channels/trials;
also accepts 1d array of spike times) -- required
phi
(angle for evaluation of derivative) -- required.
e.g. phi=[0,pi/2] giving the time and frequency derivatives
params: structure with fields tapers, pad, Fs, fpass, trialave
-optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form

106

CHAPTER 4. FUNCTION REFERENCE

t

Output:
dS
f

[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
trialave (average over trials when 1, don’t average when 0) optional. Default 0
(time grid over which the tapers are to be calculated:
this argument is useful when calling the spectrum
calculation routine from a moving window spectrogram
calculation routine). If left empty, the spike times
are used to define the grid.
(spectral derivative in form phi x frequency x channels/trials if trialave=0;
function of phi x frequency if trialave=1)
(frequencies)

This function calls:
minmaxsptimes (Section 4.48) Find the minimum and maximum of the
spike times in each channel
mtfftpt (Section 4.57) Multi-taper fourier transform for point process given
as times

This function is called by:
mtdspecgrampt (Section 4.51) Multi-taper derivative time-frequency spectrum - point process times

107

CHAPTER 4. FUNCTION REFERENCE

4.55

mtfftc

Purpose:
Multi-taper fourier transform - continuous data
Synopsis:
function J=mtfftc(data,tapers,nfft,Fs)
Comments:
Multi-taper fourier transform - continuous data
Usage:
J=mtfftc(data,tapers,nfft,Fs) - all arguments required
Input:
data (in form samples x channels/trials or a single vector)
tapers (precalculated tapers from dpss)
nfft (length of padded data)
Fs
(sampling frequency)
Output:
J (fft in form frequency index x taper index x channels/trials)

This function calls:
none This function calls no functions

This function is called by:
CrossSpecMatc (Section 4.1) Multi-taper cross-spectral matrix - another
routine, allows for multiple trials and channels
coherencyc (Section 4.8) Multi-taper coherency,cross-spectrum and individual spectra - continuous process
coherencyc unequal length trials (Section 4.9) This routine computes
the average multi-taper coherence for a given set of unequal length
segments. It is
cohmatrixc (Section 4.26) Multi-taper coherency,cross-spectral matrix continuous process
ftestc (Section 4.41) computes the F-statistic for sine wave in locally-white
noise (continuous data).
mtdspectrumc (Section 4.52) Multi-taper frequency derivative of the spectrum - continuous process

108

CHAPTER 4. FUNCTION REFERENCE
mtspectrumc (Section 4.66) Multi-taper spectrum - continuous process
mtspectrumc unequal length trials (Section 4.67) This routine computes
the multi-taper spectrum for a given set of unequal length segments.
It is
mtspectrumsegc (Section 4.70) Multi-taper segmented spectrum for a univariate continuous process
nonst stat (Section 4.76) Nonstationarity test - continuous process

109

CHAPTER 4. FUNCTION REFERENCE

4.56

mtfftpb

Purpose:
Multi-taper fourier transform - binned point process data
Synopsis:
function [J,Msp,Nsp]=mtfftpb(data,tapers,nfft)
Comments:
Multi-taper fourier transform - binned point process data
Usage:
[J,Msp,Nsp]=mtfftpb(data,tapers,nfft) - all arguments required
Input:
data
(in form samples x channels/trials or single vector)
tapers (precalculated tapers from dpss)
nfft
(length of padded data)
Output:
J (fft in form frequency index x taper index x channels/trials)
Msp (number of spikes per sample in each channel)
Nsp (number of spikes in each channel)

This function calls:
none This function calls no functions

This function is called by:
CrossSpecMatpb (Section 4.2)
coherencypb (Section 4.12) Multi-taper coherency,cross-spectrum and individual spectra - binned point process
cohmatrixpb (Section 4.27) Multi-taper coherency matrix - binned point
process
mtdspectrumpb (Section 4.53) Multi-taper spectral derivative - binned
point process
mtspectrumpb (Section 4.68) Multi-taper spectrum - binned point process
mtspectrumsegpb (Section 4.71) Multi-taper segmented spectrum for a
univariate binned point process

110

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4.57

mtfftpt

Purpose:
Multi-taper fourier transform for point process given as times
Synopsis:
function [J,Msp,Nsp]=mtfftpt(data,tapers,nfft,t,f,findx)
Comments:
Multi-taper fourier transform for point process given as times
Usage:
[J,Msp,Nsp]=mtfftpt (data,tapers,nfft,t,f,findx) - all arguments required
Input:
data
(struct array of times with dimension channels/trials;
also takes in 1d array of spike times as a column vector)
tapers
(precalculated tapers from dpss)
nfft
(length of padded data)
t
(time points at which tapers are calculated)
f
(frequencies of evaluation)
findx
(index corresponding to frequencies f)
Output:
J (fft in form frequency index x taper index x channels/trials)
Msp (number of spikes per sample in each channel)
Nsp (number of spikes in each channel)

This function calls:
none This function calls no functions

This function is called by:
CrossSpecMatpt (Section 4.3)
coherencypt (Section 4.13) Multi-taper coherency - point process times
cohmatrixpt (Section 4.28) Multi-taper coherency matrix - point process
times
mtdspectrumpt (Section 4.54) Multi-taper spectral derivative - point process times
mtspectrumpt (Section 4.69) Multi-taper spectrum - point process times
mtspectrumsegpt (Section 4.72) Multi-taper segmented spectrum for a
univariate binned point process

111

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4.58

112

mtpowerandfstatc

Purpose:
Multi-taper computation of the power and the fstatistic for a particular frequency - continuous process
Synopsis:
function [P,Fstat,f0]=mtpowerandfstatc(data,params,f0)
Comments:
Multi-taper computation of the power and the fstatistic for a particular frequency - continuous process
Usage:
[P,Fstat,f0]=mtpowerandfstatc(data,params,f0)
Input:
Note units have to be consistent. See chronux.m for more information.
data (in form samples x channels/trials or a single vector) -- required
params: structure with fields tapers, pad, Fs, fpass, err, trialave
-optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
(frequency of calculation)

f0
Output:
P
Fstat
f0

(integrated power within the frequency range of interest (trapezoidal integration))
(F-statistic)
(frequency)

CHAPTER 4. FUNCTION REFERENCE
This function calls:
none This function calls no functions

This function is called by:
none No functions call this function

113

CHAPTER 4. FUNCTION REFERENCE

4.59

mtspecgramc

Purpose:
Multi-taper time-frequency spectrum - continuous process
Synopsis:
function [S,t,f,Serr]=mtspecgramc(data,movingwin,params)
Comments:
Multi-taper time-frequency spectrum - continuous process
Usage:
[S,t,f,Serr]=mtspecgramc(data,movingwin,params)
Input:
Note units have to be consistent. Thus, if movingwin is in seconds, Fs
has to be in Hz. see chronux.m for more information.
data
(in form samples x channels/trials) -- required
movingwin
(in the form [window winstep] i.e length of moving
window and step size)
Note that units here have
to be consistent with
units of Fs - required
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Note that T has to be equal to movingwin(1).
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form

114

CHAPTER 4. FUNCTION REFERENCE

115

[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over trials/channels when 1, don’t average when 0) - optional. Default 0
Output:
S
t
f
Serr

(spectrum in form time x frequency x channels/trials if trialave=0;
in the form time x frequency if trialave=1)
(times)
(frequencies)
(error bars) only for err(1)>=1

This function calls:
mtspectrumc (Section 4.66) Multi-taper spectrum - continuous process

This function is called by:
mtspecgramtrigc (Section 4.62) Multi-taper event triggered time-frequency
spectrum - continuous process

CHAPTER 4. FUNCTION REFERENCE

4.60

mtspecgrampb

Purpose:
Multi-taper time-frequency spectrum - binned point process
Synopsis:
function [S,t,f,R,Serr]=mtspecgrampb(data,movingwin,params,fscorr)

Comments:
Multi-taper time-frequency spectrum - binned point process
Usage:
[S,t,f,R,Serr]=mtspecgrampb(data,movingwin,params,fscorr)
Input:
data
(in form samples x channels/trials or single vector) -- required
movingwin
(in the form [window,winstep] i.e length of moving
window and step size.
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Note that T has to be equal to movingwin(1).
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2

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CHAPTER 4. FUNCTION REFERENCE
err

117

(error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over trials/channnels when 1, don’t average when 0) - optional. Default 0
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
Output:
S
(spectrum in form time x frequency x channels/trials for trialave=0;
or as a function of frequency if trialave=1)
t
(times)
f
(frequencies)
R
(rate)
Serr
(error bars) - only for err(1)>=1

This function calls:
mtspectrumpb (Section 4.68) Multi-taper spectrum - binned point process

This function is called by:
mtspecgramtrigpb (Section 4.63) Multi-taper event triggered time-frequency
spectrum - binned point process

CHAPTER 4. FUNCTION REFERENCE

4.61

mtspecgrampt

Purpose:
Multi-taper time-frequency spectrum - point process times
Synopsis:
function [S,t,f,R,Serr]=mtspecgrampt(data,movingwin,params,fscorr)

Comments:
Multi-taper time-frequency spectrum - point process times
Usage:
[S,t,f,R,Serr]=mtspecgrampt(data,movingwin,params,fscorr)
Input:
data
(structure array of spike times with dimension channels/trials;
also accepts 1d array of spike times) -- required
movingwin
(in the form [window,winstep] i.e length of moving
window and step size.
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Note that T has to be equal to movingwin(1).
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.

118

CHAPTER 4. FUNCTION REFERENCE

119

Default all frequencies between 0 and Fs/2
(error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over trials/channels when 1, don’t average when 0) - optional. Default 0
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
err

Output:
S
t
f

(spectrogram with dimensions time x frequency x channels/trials if trialave=0;
dimensions time x frequency if trialave=1)
(times)
(frequencies)

Serr

(error bars) - only if err(1)>=1

This function calls:
extractdatapt (Section 4.38) Extract segements of spike times between t(1)
and t(2)
minmaxsptimes (Section 4.48) Find the minimum and maximum of the
spike times in each channel
mtspectrumpt (Section 4.69) Multi-taper spectrum - point process times

This function is called by:
mtspecgramtrigpt (Section 4.64) Multi-taper event triggered time-frequency
spectrum - point process times

CHAPTER 4. FUNCTION REFERENCE

4.62

mtspecgramtrigc

Purpose:
Multi-taper event triggered time-frequency spectrum - continuous process
Synopsis:
function [S,t,f,Serr]=mtspecgramtrigc(data,E,win,movingwin,params)

Comments:
Multi-taper event triggered time-frequency spectrum - continuous process
Usage:
[S,t,f,Serr]=mtspecgramtrigc(data,E,win,movingwin,params)
Input:
Note units have to be consistent. Thus, if movingwin is in seconds, Fs
has to be in Hz. see chronux.m for more information.
data
(single channel data) -- required
E
(event times) -- required
win
(in the form [winl winr] i.e window around each event)
required
movingwin
(in the form [window winstep] i.e length of moving
window and step size) required
Note that units for the windows have
to be consistent with
units of Fs
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Note that T has to be equal to movingwin(1).
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding

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CHAPTER 4. FUNCTION REFERENCE
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over events when 1, don’t average when 0) - optional. Default 0
Output:
S
t
f
Serr

(triggered spectrum in form time x frequency x events for trialave=0;
or in the form time x frequency trialave=1)
(times)
(frequencies)
(error bars) only for err(1)>=1

This function calls:
createdatamatc (Section 4.30) Helper function to create an event triggered
matrix from univariate
mtspecgramc (Section 4.59) Multi-taper time-frequency spectrum - continuous process

This function is called by:
none No functions call this function

121

CHAPTER 4. FUNCTION REFERENCE

4.63

mtspecgramtrigpb

Purpose:
Multi-taper event triggered time-frequency spectrum - binned point process
Synopsis:
function [S,t,f,R,Serr]=mtspecgramtrigpb(data,E,win,movingwin,params,fscorr)

Comments:
Multi-taper event triggered time-frequency spectrum - binned point process
Usage:
[S,t,f,R,Serr]=mtspecgramtrigpb(data,E,win,movingwin,params,fscorr)
Input:
data
(single channel data vector) -- required
E
(event times) - required
win
(in the form [winl,winr] i.e window around each event
required
movingwin
(in the form [window,winstep] i.e length of moving
window and step size) required
Note that units for the windows have
to be consistent with
units of Fs
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Note that T has to be equal to movingwin(1).
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT

122

CHAPTER 4. FUNCTION REFERENCE
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over events when 1, don’t average when 0) - optional. Default 0
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
Output:
S
(triggered time-frequency spectrum in form time x frequency x events if segave=0;
or in the form time x frequency segave=1)
t
(times)
f
(frequencies)
R
(spike rate)
Serr
(error bars) - only for err(1)>=1

This function calls:
createdatamatpb (Section 4.31)
mtspecgrampb (Section 4.60) Multi-taper time-frequency spectrum - binned
point process

This function is called by:
none No functions call this function

123

CHAPTER 4. FUNCTION REFERENCE

4.64

mtspecgramtrigpt

Purpose:
Multi-taper event triggered time-frequency spectrum - point process times
Synopsis:
function [S,t,f,R,Serr]=mtspecgramtrigpt(data,E,win,movingwin,params,fscorr)

Comments:
Multi-taper event triggered time-frequency spectrum - point process times
Usage:
[S,t,f,R,Serr]=mtspecgramtrigpt(data,E,win,movingwin,params,fscorr)
Input:
data
(univariate spike data -1d structure array of spike times;
also accepts 1d array of spike times) -- required
E
(event times) - required
win
(in the form [winl,winr] i.e window around each event
required
movingwin
(in the form [window winstep] i.e length of moving
window and step size) required
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Note that T has to be equal to movingwin(1).
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.

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CHAPTER 4. FUNCTION REFERENCE
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over events when 1, don’t average when 0) - optional. Default 0
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
Output:
S
t
f
R
Serr

(Spectrogram with dimensions time x frequency x events if trialave=0;
dimensions time x frequency if trialave=1)
(times)
(frequencies)
(spike rate)
(error bars)-only if err(1)>=1

This function calls:
createdatamatpt (Section 4.32) Helper function to create an event triggered matrix from a single
mtspecgrampt (Section 4.61) Multi-taper time-frequency spectrum - point
process times

This function is called by:
none No functions call this function

125

CHAPTER 4. FUNCTION REFERENCE

4.65

mtspectrum of spectrumc

Purpose:
Multi-taper segmented, second spectrum (spectrum of the log spectrum) for
a continuous process
Synopsis:
function [SS,tau]=mtspectrum of spectrumc(data,win,tapers2spec,params)

Comments:
Multi-taper segmented, second spectrum (spectrum of the log spectrum) for a continuous process
This routine computes the second spectrum by explicitly evaluating the
Fourier transform (since the spectrum is symmetric in frequency, it uses
a cosine transform)
Usage:
[SS,tau]=mtspectrum_of_spectrumc(data,win,tapers2spec,params)
Input:
Note units have to be consistent. See chronux.m for more information.
data (single channel) -- required
win (duration of the segments) - required.
tapers2spec (tapers used for the spectrum of spectrum computation) required in the form [use TW K] - Note that spectrum of the
spectrum involves computing two Fourier transforms. While the first
transform (of the original data) is always computed using the
multi-taper method, the current routine allows the user to specify
whether or not to use this method for the second transform. use=1
means use tapers, use=anything other than 1 means do not use the
multitaper method. If use=1, then tapers2spec controls the
smoothing for the second Fourier transform. Otherwise, a direct
Fourier transform is computed.
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.

126

CHAPTER 4. FUNCTION REFERENCE
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and
Fs/2
Output:
SS
tau

(second spectrum in form frequency x segments x trials x channels
if segave=0; in the form frequency x trials x channels if segave=1)
(frequencies)

This function calls:
createdatamatc (Section 4.30) Helper function to create an event triggered
matrix from univariate
mtspectrumc (Section 4.66) Multi-taper spectrum - continuous process
mtspectrumsegc (Section 4.70) Multi-taper segmented spectrum for a univariate continuous process

This function is called by:
none No functions call this function

127

CHAPTER 4. FUNCTION REFERENCE

4.66

128

mtspectrumc

Purpose:
Multi-taper spectrum - continuous process
Synopsis:
function [S,f,Serr]=mtspectrumc(data,params)
Comments:
Multi-taper spectrum - continuous process
Usage:
[S,f,Serr]=mtspectrumc(data,params)
Input:
Note units have to be consistent. See chronux.m for more information.
data (in form samples x channels/trials) -- required
params: structure with fields tapers, pad, Fs, fpass, err, trialave
-optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over trials/channels when 1, don’t average when 0) - optional. Default 0
Output:

CHAPTER 4. FUNCTION REFERENCE
S
f
Serr

(spectrum in form frequency x channels/trials if trialave=0;
in the form frequency if trialave=1)
(frequencies)
(error bars) only for err(1)>=1

This function calls:
mtfftc (Section 4.55) Multi-taper fourier transform - continuous data

This function is called by:
ftestc (Section 4.41) computes the F-statistic for sine wave in locally-white
noise (continuous data).
mtspecgramc (Section 4.59) Multi-taper time-frequency spectrum - continuous process
mtspectrum of spectrumc (Section 4.65) Multi-taper segmented, second
spectrum (spectrum of the log spectrum) for a continuous process
mtspectrumtrigc (Section 4.73) Multi-taper event triggered time-frequency
spectrum - continuous process
rmlinesc (Section 4.85) removes significant sine waves from data (continuous data).

129

CHAPTER 4. FUNCTION REFERENCE

mtspectrumc unequal length trials

4.67

Purpose:
This routine computes the multi-taper spectrum for a given set of unequal
length segments. It is
Synopsis:
function [ S, f, Serr ]= mtspectrumc unequal length trials( data,
movingwin, params, sMarkers )
Comments:
This routine computes the multi-taper spectrum for a given set of unequal length segments. It is
based on modifications to the Chronux routines. The segments are continuously structured in the
data matrix, with the segment boundaries given by markers. Below,
movingwin is used in a non-overlaping way to partition each segment into
various windows. Th spectrum is evaluated for each window, and then the
window spectrum estimates averaged. Further averaging is conducted by
repeating the process for each segment.
Inputs:
data = data( samples, channels )- here segments must be stacked
as explained in the email
movingwin = [window winstep] i.e length of moving
window and step size. Note that units here have
to be consistent with units of Fs. If Fs=1 (ie normalized)
then [window winstep]should be in samples, or else if Fs is
unnormalized then they should be in time (secs).
sMarkers = N x 2 array of segment start & stop marks. sMarkers(n, 1) = start
sample index; sMarkers(n,2) = stop sample index for the nth segment
params = see Chronux help on mtspecgramc
Output:
S
f
Serr

frequency x channels
frequencies x 1
(error bars) only for err(1)>=1

This function calls:
mtfftc (Section 4.55) Multi-taper fourier transform - continuous data

This function is called by:
none No functions call this function

130

CHAPTER 4. FUNCTION REFERENCE

4.68

131

mtspectrumpb

Purpose:
Multi-taper spectrum - binned point process
Synopsis:
function [S,f,R,Serr]=mtspectrumpb(data,params,fscorr)
Comments:
Multi-taper spectrum - binned point process
Usage:
[S,f,R,Serr]=mtspectrumpb(data,params,fscorr)
Input:
data (in form samples x channels/trials or a single vector) -- required
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over channels/trials when 1, don’t average when 0) - optional. Default 0
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional

CHAPTER 4. FUNCTION REFERENCE
(available only for spikes). Defaults 0.
Output:
S
f
R
Serr

(spectrum in form frequency x channels/trials if trialave=0;
as a function of frequency if trialave=1)
(frequencies)
(spike rate)
(error bars) - only for err(1)>=1

This function calls:
mtfftpb (Section 4.56) Multi-taper fourier transform - binned point process
data

This function is called by:
mtspecgrampb (Section 4.60) Multi-taper time-frequency spectrum - binned
point process
mtspectrumtrigpb (Section 4.74) Multi-taper event triggered time-frequency
spectrum - binned point process

132

CHAPTER 4. FUNCTION REFERENCE

4.69

133

mtspectrumpt

Purpose:
Multi-taper spectrum - point process times
Synopsis:
function [S,f,R,Serr]=mtspectrumpt(data,params,fscorr,t)
Comments:
Multi-taper spectrum - point process times
Usage:
[S,f,R,Serr]=mtspectrumpt(data,params,fscorr,t)
Input:
data
(structure array of spike times with dimension channels/trials;
also accepts 1d array of spike times) -- required
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over channels/trials when 1, don’t average when 0) - optional. Default 0
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or

CHAPTER 4. FUNCTION REFERENCE

t

Output:
S
f
R
Serr

1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
(time grid over which the tapers are to be calculated:
this argument is useful when calling the spectrum
calculation routine from a moving window spectrogram
calculation routine). If left empty, the spike times
are used to define the grid.
(spectrum with dimensions frequency x channels/trials if trialave=0;
dimension frequency if trialave=1)
(frequencies)
(rate)
(error bars) - only if err(1)>=1

This function calls:
minmaxsptimes (Section 4.48) Find the minimum and maximum of the
spike times in each channel
mtfftpt (Section 4.57) Multi-taper fourier transform for point process given
as times

This function is called by:
mtspecgrampt (Section 4.61) Multi-taper time-frequency spectrum - point
process times
mtspectrumtrigpt (Section 4.75) Multi-taper time-frequency spectrum point process times

134

CHAPTER 4. FUNCTION REFERENCE

4.70

mtspectrumsegc

Purpose:
Multi-taper segmented spectrum for a univariate continuous process
Synopsis:
function [S,f,varS,C,Serr]=mtspectrumsegc(data,win,params,segave)

Comments:
Multi-taper segmented spectrum for a univariate continuous process
Usage:
[S,f,varS,C,Serr]=mtspectrumsegc(data,win,params,segave)
Input:
Note units have to be consistent. See chronux.m for more information.
data (single channel) -- required
win (duration of the segments) - required.
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.

135

CHAPTER 4. FUNCTION REFERENCE

136

trialave - not used
segave - optional 0 for don’t average over segments, 1 for average - default
1
Output:
S
(spectrum in form frequency x segments if segave=0; in the form frequency if segave=1)
f
(frequencies)
varS
(variance of the log spectrum)
C
(covariance matrix of the log spectrum - frequency x
frequency matrix)
Serr
(error bars) only for err(1)>=1

This function calls:
createdatamatc (Section 4.30) Helper function to create an event triggered
matrix from univariate
mtfftc (Section 4.55) Multi-taper fourier transform - continuous data

This function is called by:
mtspectrum of spectrumc (Section 4.65) Multi-taper segmented, second
spectrum (spectrum of the log spectrum) for a continuous process
rmlinesmovingwinc (Section 4.86) fits significant sine waves to data (continuous data) using overlapping windows.

CHAPTER 4. FUNCTION REFERENCE

4.71

mtspectrumsegpb

Purpose:
Multi-taper segmented spectrum for a univariate binned point process
Synopsis:
function [S,f,R,varS,zerosp,C,Serr]=mtspectrumsegpb(data,win,params,segave,fscorr)

Comments:
Multi-taper segmented spectrum for a univariate binned point process
Usage:
[S,f,R,varS,zerosp,C,Serr]=mtspectrumsegpb(data,win,params,segave,fscorr)
Input:
Note units have to be consistent. See chronux.m for more information.
data (single vector) -- required
win (duration of the segments) - required.
params: structure with fields tapers, pad, Fs, fpass, err
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.

137

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138

segave (1 for averaging across segments, 0 otherwise; default 1)
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
Output:
S
(spectrum in form frequency x segments if segave=0; as a function of frequency if segave=1)
f
(frequencies)
R
(spike rate)
varS
(variance of the log spectrum)
zerosp (0 for segments in which spikes were found, 1 for segments
in which there are no spikes)
C
(covariance matrix of the log spectrum - frequency x
frequency matrix)
Serr
(error bars) - only for err(1)>=1

This function calls:
createdatamatpb (Section 4.31)
mtfftpb (Section 4.56) Multi-taper fourier transform - binned point process
data

This function is called by:
none No functions call this function

CHAPTER 4. FUNCTION REFERENCE

4.72

mtspectrumsegpt

Purpose:
Multi-taper segmented spectrum for a univariate binned point process
Synopsis:
function [S,f,R,varS,zerosp,C,Serr]=mtspectrumsegpt(data,win,params,segave,fscorr)

Comments:
Multi-taper segmented spectrum for a univariate binned point process
Usage:
[S,f,R,varS,zerosp,C,Serr]=mtspectrumsegpt(data,win,params,segave,fscorr)
Input:
Note units have to be consistent. See chronux.m for more information.
data (structure array of one channel of spike times;
also accepts 1d vector of spike times) -- required
win (duration of the segments) - required.
params: structure with fields tapers, pad, Fs, fpass, err
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars

139

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140

[0 p] or 0 - no error bars) - optional. Default 0.
segave - (0 for don’t average over segments, 1 for average) - optional - default 1
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
Output:
S
(spectrum in form frequency x segments if segave=0; function of frequency if segave=1)
f
(frequencies)
R
(spike rate)
varS
(variance of the spectrum as a function of frequency)
zerosp (0 for segments in which spikes were found, 1 for segments
C
(covariance matrix of the log spectrum - frequency x
frequency matrix)
Serr
(error bars) - only if err(1)>=1

This function calls:
createdatamatpt (Section 4.32) Helper function to create an event triggered matrix from a single
minmaxsptimes (Section 4.48) Find the minimum and maximum of the
spike times in each channel
mtfftpt (Section 4.57) Multi-taper fourier transform for point process given
as times

This function is called by:
none No functions call this function

CHAPTER 4. FUNCTION REFERENCE

4.73

mtspectrumtrigc

Purpose:
Multi-taper event triggered time-frequency spectrum - continuous process
Synopsis:
function [S,f,Serr]=mtspectrumtrigc(data,E,win,params)
Comments:
Multi-taper event triggered time-frequency spectrum - continuous process
Usage:
[S,f,Serr]=mtspectrumtrigc(data,E,win,params)
Input:
Note units have to be consistent. See chronux.m for more information.
data
(single channel) -- required
E
(event times) -- required
win
(in the form [winl winr] i.e window around each event
required)
Note that units here have
to be consistent with
units of Fs
params: structure with fields tapers, pad, Fs, fpass, err, trialave
-optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form

141

CHAPTER 4. FUNCTION REFERENCE
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over events when 1, don’t average when 0) - optional. Default 0
Output:
S
f
Serr

(triggered spectrum in form frequency x events for trialave=0 or as a function of frequency for trialave=1)
(frequencies)
(error bars) only for err(1)>=1

This function calls:
createdatamatc (Section 4.30) Helper function to create an event triggered
matrix from univariate
mtspectrumc (Section 4.66) Multi-taper spectrum - continuous process

This function is called by:
none No functions call this function

142

CHAPTER 4. FUNCTION REFERENCE

4.74

mtspectrumtrigpb

Purpose:
Multi-taper event triggered time-frequency spectrum - binned point process
Synopsis:
function [S,f,R,Serr]=mtspectrumtrigpb(data,E,win,params,fscorr)

Comments:
Multi-taper event triggered time-frequency spectrum - binned point process
Usage:
[S,f,R,Serr]=mtspectrumtrigpb(data,E,win,params,fscorr)
Input:
data
(single channel data) -- required
E
(event times) - required
win
(in the form [winl winr] i.e window around each event
required
Note that units here have
to be consistent with
units of Fs
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form

143

CHAPTER 4. FUNCTION REFERENCE
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over events when 1, don’t average when 0) optional. Default 0
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
Output:
S
(triggered spectrum in form frequency x events for trialave=0,
or as a function of frequency for trialave=1)
f
(frequencies)
R
(spike rate)
Serr
(error bars) - only for err(1)>=1

This function calls:
createdatamatpb (Section 4.31)
mtspectrumpb (Section 4.68) Multi-taper spectrum - binned point process

This function is called by:
none No functions call this function

144

CHAPTER 4. FUNCTION REFERENCE

4.75

mtspectrumtrigpt

Purpose:
Multi-taper time-frequency spectrum - point process times
Synopsis:
function [S,f,R,Serr]=mtspectrumtrigpt(data,E,win,params,fscorr)

Comments:
Multi-taper time-frequency spectrum - point process times
Usage:
[S,f,R,Serr]=mtspectrumtrigpt(data,E,win,params,fscorr)
Input:
data
(structure array of one channel of spike times;
also accepts 1d column vector of spike times) -- required
E
(event times) - required
win
(in the form [winl winr] i.e window around each event)-required
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs
(sampling frequency) - optional. Default 1.
fpass
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2

145

CHAPTER 4. FUNCTION REFERENCE
err

(error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over events when 1, don’t average when 0) default 0
fscorr
(finite size corrections, 0 (don’t use finite size corrections) or
1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
Output:
S
f
R
Serr

(triggered spectrum in form frequency x events if trialave=0;
function of frequency if trialave=1)
(frequencies)
(spike rate)
(error bars) - only for err(1)>=1

This function calls:
createdatamatpt (Section 4.32) Helper function to create an event triggered matrix from a single
mtspectrumpt (Section 4.69) Multi-taper spectrum - point process times

This function is called by:
none No functions call this function

146

CHAPTER 4. FUNCTION REFERENCE

4.76

nonst stat

Purpose:
Nonstationarity test - continuous process
Synopsis:
function sigma = nonst stat(data,A,sumV,params)
Comments:
Nonstationarity test - continuous process
Usage:
sigma=nonst_test(data,A,sumV,params)
Input:
Note units have to be consistent. See chronux.m for more information.
data (1d array in samples) -- required
A
quadratic coefficient matrix - (Compute this separately since
the computation is time consuming - [A,sumV]=quadcof(N,NW,order). order
has to < 4NW.)
sumV
sum of the quadratic inverse basis vectors
params: structure with fields tapers, pad, Fs, fpass, err, trialave
-optional
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
pad

Fs
Output:
sigma

(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
(sampling frequency) - optional. Default 1.
(nonstationarity index Thomson, 2000)

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This function calls:
mtfftc (Section 4.55) Multi-taper fourier transform - continuous data

This function is called by:
none No functions call this function

148

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4.77

padNaN

Purpose:
Creates a padded data matrix from input structural array of spike times
Synopsis:
function data=padNaN(data)
Comments:
Creates a padded data matrix from input structural array of spike times
pads with NaN
Usage: data=padNaN(data)
Input:
data : structural array of spike times
Output:
data : data matrix (zero padded)

This function calls:
none This function calls no functions

This function is called by:
countsig (Section 4.29) Give the program two spike data sets and one
isi (Section 4.44) Calculate the inter-spike-interval histogram
psth (Section 4.82) function to plot trial averaged rate smoothed by

149

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4.78

plot matrix

Purpose:
Function to plot a time-frequency matrix X. Time and frequency axes are in
t and f.
Synopsis:
function plot matrix(X,t,f,plt,Xerr)
Comments:
Function to plot a time-frequency matrix X. Time and frequency axes are in t and f.
If error bars are specified in Xerr,
it also plots them. Xerr contains upper and lower confidence intervals
on X.
Usage: plot_matrix(X,t,f,plt,Xerr)
Inputs:
X: input vector as a function of time and frequency (t x f)
t: t axis grid for plot. Default [1:size(X,1)]
f: f axis grid for plot. Default. [1:size(X,2)]
plt: ’l’ for log, ’n’ for no log.
Xerr: lower and upper confidence intervals for X1: lower/upper x t x f.

This function calls:
none This function calls no functions

This function is called by:
none No functions call this function

150

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4.79

plot vector

Purpose:
Function to plot a frequency dependent vector X. If error bars are specified
in Xerr,
Synopsis:
function plot vector(X,f,plt,Xerr,c,w)
Comments:
Function to plot a frequency dependent vector X. If error bars are specified in Xerr,
it also plots them. Xerr can either contain upper and lower confidence intervals
on X, or simply a theoretical confidence level (for the coherence). Used
to plot the spectrum and coherency.
Usage: plot_vector(X,f,plt,Xerr,c)
Inputs:
X: input vector as a function of frequency (f), see third argument
f: f axis grid for plot. Default. [1:length(X)]
plt: ’l’ for log, ’n’ for no log.
Xerr: lower and upper confidence intervals for X1: lower/upper x f. Or
simply a single number specifying an f-independent confidence
level.
c: controls the color of the plot - input ’b’,’g’,’r’ etc. Default ’b’
w: controls the width of the lines - input 1, 1.5, 2 etc

This function calls:
none This function calls no functions

This function is called by:
none No functions call this function

151

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4.80

plotsig

Purpose:
Function to plot C where it is higher than a threshold sig
Synopsis:
function plotsig(C,sig,t,f,c)
Comments:
Function to plot C where it is higher than a threshold sig
useful for plotting coherence
Usage: plotsig(C,sig,t,f)
Inputs:
C: input array t x f - also works for a single vector
sig: significance level
t: t axis grid for plot
f: f axis grid for plot.
c: color to use (default blue)-only meaningful for a line plot

This function calls:
none This function calls no functions

This function is called by:
none No functions call this function

152

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4.81

plotsigdiff

Purpose:
Function to plot significant differences between two time-frequency arrays
X1 and X2
Synopsis:
function [mask,Xdiff]=plotsigdiff(X1,X1err,X2,X2err,plt,t,f)
Comments:
Function to plot significant differences between two time-frequency arrays X1 and X2
given errors X1err, X2err.
Usage: mask=plotsigdiff(X1,X1err,X2,X2err,plt,t,f)
X1 err and X2err contain upper and lower confidence intervals for X1 and X2
The plot generated is shows X1-X2 where the difference is significant
either in dB or on a linear scale.
Inputs:
X1: input array t x f. Can also be a function of just the frequency.
X1err: lower and upper confidence intervals for X1: lower/upper x t x f
X2: input array t x f. if vector then as row vector
X2err: lower and upper condidence intervals for X2: lower/upper x t x f
plt: ’l’ for log, ’nl’ for no log,’n’ for no plot at all.
t: t axis grid for plot. If X1,X2 are vectors, then specify t=1.
f: f axis grid for plot.
Outputs:
mask: +1 for all t-f (or f) indices for which the X1 significantly greater than
X2, -1 for all t-f (or f) indices for which X1 is significantly less than X2,
and zero otherwise
Xdiff: X1-X2

This function calls:
none This function calls no functions

This function is called by:
none No functions call this function

153

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4.82

psth

Purpose:
function to plot trial averaged rate smoothed by
Synopsis:
function [R,t,E] = psth(data,sig,plt,T,err,t)
Comments:
function to plot trial averaged rate smoothed by
a Gaussian kernel - visual check on stationarity
Usage: [R,t,E] = psth(data,sig,plt,T,err,t)
Inputs:
Note that all times have to be consistent. If data
is in seconds, so must be sig and t. If data is in
samples, so must sig and t. The default is seconds.
data
structural array of spike times
sig
std dev of Gaussian (default 50ms)
(minus indicates adaptive with
approx width equal to mod sig)
plt = ’n’|’r’ etc
(default ’r’)
T is the time interval (default all)
err - 0 = none
1 = Poisson
2 = Bootstrap over trials (default)
(both are based on 2* std err rather than 95%)
t
= times to evaluate psth at
The adaptive estimate works by first estimating
the psth with a fixed kernel width (-sig) it
then alters the kernel width so that the number
of spikes falling under the kernel is the same on
average but is time dependent. Reagions rich
in data therefore have their kernel width reduced
Outputs:
R = rate
t = times
E = errors (standard error)

This function calls:
padNaN (Section 4.77) Creates a padded data matrix from input structural
array of spike times

This function is called by:

154

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none No functions call this function

155

CHAPTER 4. FUNCTION REFERENCE

4.83

quadcof

Purpose:
Helper function to calculate the nonstationary quadratic inverse matrix
Synopsis:
function [A,sumV] = quadcof(N,NW,order)
Comments:
Helper function to calculate the nonstationary quadratic inverse matrix
Usage: [A,sumV] = quadcof(N,NW,order)
N
(number of samples)
NW: Time bandwidth product
order: order (number of coefficients, upto 4NW)
Outputs:
A: quadratic inverse coefficient matrix
sumV: sum of the quadratic inverse eigenvectors

This function calls:
quadinv (Section 4.84) calculates the quadratic inverse eigenvectors

This function is called by:
none No functions call this function

156

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4.84

quadinv

Purpose:
calculates the quadratic inverse eigenvectors
Synopsis:
function [V,E] = quadinv(N,NW)
Comments:
calculates the quadratic inverse eigenvectors
Input
N: number of samples
NW: time-bandwidth product
Output
V: The quadratic inverse eigenvectors
E: the quadratic inverse eigenvalues

This function calls:
none This function calls no functions

This function is called by:
quadcof (Section 4.83) Helper function to calculate the nonstationary quadratic
inverse matrix

157

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4.85

rmlinesc

Purpose:
removes significant sine waves from data (continuous data).
Synopsis:
function data=rmlinesc(data,params,p,plt,f0)
Comments:
removes significant sine waves from data (continuous data).
Usage: data=rmlinesc(data,params,p,plt,f0)
Inputs:
Note that units of Fs, fpass have to be consistent.
data
(data in [N,C] i.e. time x channels/trials or a single vector) - required.
params
structure containing parameters - params has the
following fields: tapers, Fs, fpass, pad
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Fs

(sampling frequency) -- optional. Defaults to 1.
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
pad
(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
p
(P-value for F-test) - optional. Defaults to 0.05/N
where N is data length. This corresponds to a false detect
probability of approximately 0.05
fpass

plt

(y/n for plot and no plot respectively)

158

CHAPTER 4. FUNCTION REFERENCE
f0

Outputs:
data

frequencies at which you want to remove the
lines - if unspecified the program uses the f statistic
to determine appropriate lines.

(data with significant lines removed)

This function calls:
fitlinesc (Section 4.40) fits significant sine waves to data (continuous data).
mtspectrumc (Section 4.66) Multi-taper spectrum - continuous process

This function is called by:
none No functions call this function

159

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4.86

160

rmlinesmovingwinc

Purpose:
fits significant sine waves to data (continuous data) using overlapping windows.
Synopsis:
function [datac,datafit,Amps,freqs]=rmlinesmovingwinc(data,movingwin,tau,params,p,plt,f0)

Comments:
fits significant sine waves to data (continuous data) using overlapping windows.
Usage: [datac,datafit]=rmlinesmovingwinc(data,movingwin,tau,params,p,plt)
Inputs:
Note that units of Fs, fpass have to be consistent.
data
(data in [N,C] i.e. time x channels/trials or as a single vector) - required.
movingwin
(in the form [window winstep] i.e length of moving
window and step size)
Note that units here have
to be consistent with
units of Fs - required
tau
parameter controlling degree of smoothing for the amplitudes - we use the
function 1-1/(1+exp(-tau*(x-Noverlap/2)/Noverlap) in the region of overlap to smooth
the sinewaves across the overlap region. Noverlap is the number of points
in the overlap region. Increasing tau leads to greater overlap smoothing,
typically specifying tau~10 or higher is reasonable. tau=1 gives an almost
linear smoothing function. tau=100 gives a very steep sigmoidal. The default is tau=10.
params
structure containing parameters - params has the
following fields: tapers, Fs, fpass, pad
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Note that T has to be equal to movingwin(1).
Fs

(sampling frequency) -- optional. Defaults to 1.

CHAPTER 4. FUNCTION REFERENCE
fpass

(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
pad
(padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
p
(P-value to calculate error bars for) - optional.
Defaults to 0.05/Nwin where Nwin is length of window which
corresponds to a false detect probability of approximately 0.05.
plt
(y/n for plot and no plot respectively) - default no
plot.
f0
frequencies at which you want to remove the
lines - if unspecified the program uses the f statistic
to determine appropriate lines.
Outputs:
datafit
datac

(fitted sine waves)
(cleaned up data)

This function calls:
fitlinesc (Section 4.40) fits significant sine waves to data (continuous data).
mtspectrumsegc (Section 4.70) Multi-taper segmented spectrum for a univariate continuous process

This function is called by:
none No functions call this function

161

CHAPTER 4. FUNCTION REFERENCE

4.87

runline

Purpose:
Running line fit (local linear regression)
Synopsis:
function y line=runline(y,n,dn)
Comments:
Running line fit (local linear regression)
Usage: y_line=runline(y,n,dn);
Inputs:
y: input 1-d time series (real)
n: length of running window in samples
dn: stepsize of window in samples
Outputs:
y_line: local line fit to data

This function calls:
none This function calls no functions

This function is called by:
locdetrend (Section 4.46) Remove running line fit (using local linear regression)continuous
locsmooth (Section 4.47) Running line fit (using local linear regression) 1d only, continuous

162

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4.88

specerr

Purpose:
Function to compute lower and upper confidence intervals on the spectrum
Synopsis:
function Serr=specerr(S,J,err,trialave,numsp)
Comments:
Function to compute lower and upper confidence intervals on the spectrum
Usage: Serr=specerr(S,J,err,trialave,numsp)
Outputs: Serr (Serr(1,...) - lower confidence level, Serr(2,...) upper confidence level)
Inputs:
S - spectrum
J - tapered fourier transforms
err - [errtype p] (errtype=1 - asymptotic estimates; errchk=2 - Jackknife estimates;
p - p value for error estimates)
trialave - 0: no averaging over trials/channels
1 : perform trial averaging
numsp
- number of spikes in each channel. specify only when finite
size correction required (and of course, only for point
process data)
Outputs:
Serr - error estimates. Only for err(1)>=1. If err=[1 p] or [2 p] Serr(...,1) and Serr(...,2)
contain the lower and upper error bars with the specified method.

This function calls:
none This function calls no functions

This function is called by:
none No functions call this function

163

CHAPTER 4. FUNCTION REFERENCE

4.89

spsvd

Purpose:
Space frequency SVD of input data - continuous processes
Synopsis:
function [sv,sp,fm] = spsvd(data,params,mdkp)
Comments:
Space frequency SVD of input data - continuous processes
Usage: [sv,sp,fm] = spsvd(data,params,mdkp)
Inputs:
data
(data matrix in timexchannels form)-required
params
structure containing parameters - params has the
following fields: tapers, Fs, fpass, pad
tapers : precalculated tapers from dpss or in the one of the following
forms:
(1) A numeric vector [TW K] where TW is the
time-bandwidth product and K is the number of
tapers to be used (less than or equal to
2TW-1).
(2) A numeric vector [W T p] where W is the
bandwidth, T is the duration of the data and p
is an integer such that 2TW-p tapers are used. In
this form there is no default i.e. to specify
the bandwidth, you have to specify T and p as
well. Note that the units of W and T have to be
consistent: if W is in Hz, T must be in seconds
and vice versa. Note that these units must also
be consistent with the units of params.Fs: W can
be in Hz if and only if params.Fs is in Hz.
The default is to use form 1 with TW=3 and K=5
Fs
fpass

pad
-1
to

mdkp

Outputs:
sv sp fm

(number of
maximum

(sampling frequency) -- optional. Defaults to 1.
(frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
(padding factor for the FFT) - optional (can take values -1,0,1,2...).
corresponds to no padding, 0 corresponds to padding
the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
dimensions to be kept)-optional. Default is the
possible modes determined by taper parameters

: singular values, space modes, frequency modes

This function calls:

164

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none This function calls no functions

This function is called by:
none No functions call this function

165

CHAPTER 4. FUNCTION REFERENCE

4.90

sta

Purpose:
Spike Triggered Average
Synopsis:
function[s,t,E] = sta(data spk,data lfp,smp,plt,w,T,D,err)
Comments:
Spike Triggered Average
Usage: [s,t,E] = sta(data_spk,data_lfp,smp,plt,w,T,D,err)
Inputs
Note that all times have to be consistent. If data_spk
is in seconds, so must be sig and t. If data_spk is in
samples, so must sig and t. The default is seconds.
data_spk
data_lfp

- strucuture array of spike times data
or NaN padded matrix
- array of lfp data(samples x trials)

Optional...
plt ’n’|’r’ etc
width kernel smoothing in s
T = [-0.1 0.1] - extract this range about each spk
D = plot spike triggered average out to [D1 D2]
err = calcluate error bars (bootstrap)
Outputs:
s
t
E

spike triggered average
times
bootstrap standard err

This function calls:
none This function calls no functions

This function is called by:
staogram (Section 4.91)

166

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4.91

167

staogram

Synopsis:
function[S,tau,tc] = staogram(data spk,data lfp,smp,plt,Tc,Tinc,Tw,w,D)

Comments:
staogram : calculates a moving window spike triggered ave %
Usage:[S,tau,tc] = staogram(data_spk,data_lfp,smp,plt,Tc,Tinc,Tw,w,D)
******** INPUT *********
Note that all times have to be consistent. If data_spk
is in seconds, so must be sig and t. If data_spk is in
samples, so must sig and t. The default is seconds.
data_spk
data_lfp
smp

- strucuture array of spike times data
- array of lfp data(samples x trials)
- lfp times of samples

Optional...
Parameter
plt

’y’|’n’

’y’ standard staogram
’n’ no plot
Tc = start and end times (centres)
Tinc = time increment between windows
Tw = time window width
w = smoothing width in seconds
D = plot sta out to on axis [D(1) D(2)] s
******** OUTPUT ********
S spike triggered average
tau - lag
tc - bin centers

This function calls:
sta (Section 4.90) Spike Triggered Average

This function is called by:
none No functions call this function

whole trial
0.1
0.3

CHAPTER 4. FUNCTION REFERENCE

4.92

168

two group test coherence

Purpose:
function [dz,vdz,Adz]=two group test coherence(J1c1,J2c1,J1c2,J2c2,p)
Synopsis:
function [dz,vdz,Adz]=two group test coherence(J1c1,J2c1,J1c2,J2c2,p,plt,f)

Comments:
function [dz,vdz,Adz]=two_group_test_coherence(J1c1,J2c1,J1c2,J2c2,p)
Test the null hypothesis (H0) that data sets J1c1,J2c1,J1c2,J2c2 in
two conditions c1,c2 have equal population coherence
Usage:
[dz,vdz,Adz]=two_sample_test_coherence(J1c1,J2c1,J1c2,J2c2,p)
Inputs:
J1c1
tapered fourier transform of dataset
J2c1
tapered fourier transform of dataset
J1c2
tapered fourier transform of dataset
J2c2
tapered fourier transform of dataset
p
p value for test (default: 0.05)
plt
’y’ for plot and ’n’ for no plot
f
frequencies (useful for plotting)

1
1
1
1

in
in
in
in

condition
condition
condition
condition

1
1
2
2

Dimensions: J1c1,J2c2: frequencies x number of samples in condition 1
J1c2,J2c2: frequencies x number of samples in condition 2
number of samples = number of trials x number of tapers
Outputs:
dz
test statistic (will be distributed as N(0,1) under H0
vdz
Arvesen estimate of the variance of dz
Adz
1/0 for accept/reject null hypothesis of equal population
coherences based dz ~ N(0,1)
Note: all outputs are functions of frequency
References: Arvesen, Jackkknifing U-statistics, Annals of Mathematical
Statisitics, vol 40, no. 6, pg 2076-2100 (1969)

This function calls:
none This function calls no functions
This function is called by:
none No functions call this function

CHAPTER 4. FUNCTION REFERENCE

4.93

two group test spectrum

Purpose:
function [dz,vdz,Adz]=two group test spectrum(J1,J2,p)
Synopsis:
function [dz,vdz,Adz]=two group test spectrum(J1,J2,p,plt,f)
Comments:
function [dz,vdz,Adz]=two_group_test_spectrum(J1,J2,p)
Test the null hypothesis (H0) that data sets J1, J2 in
two conditions c1,c2 have equal population spectrum
Usage:
[dz,vdz,Adz]=two_sample_test_spectrum(J1,J2,p)
Inputs:
J1
tapered fourier transform in condition 1
J2
tapered fourier transform in condition 2
p
p value for test (default: 0.05)
plt
’y’ for plot and ’n’ for no plot
f
frequencies (useful for plotting)

Dimensions: J1: frequencies x number of samples in condition 1
J2: frequencies x number of samples in condition 2
number of samples = number of trials x number of tapers
Outputs:
dz
test statistic (will be distributed as N(0,1) under H0
vdz
Arvesen estimate of the variance of dz
Adz
1/0 for accept/reject null hypothesis of equal population
coherences based dz ~ N(0,1)

Note: all outputs are functions of frequency
References: Arvesen, Jackkknifing U-statistics, Annals of Mathematical
Statisitics, vol 40, no. 6, pg 2076-2100 (1969)

This function calls:
none This function calls no functions

This function is called by:
none No functions call this function

169

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170

CHAPTER 4. FUNCTION REFERENCE

171

Bibliography
[1] Hemant Bokil, Bijan Pesaran, Richard A. Andersen, and Partha P. Mitra. A method for detection and classification of events in neural activity. IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING,
53:1678–1687, 2006.
[2] Hemant Bokil, Keith Purpura, Jan-Mathijs Schofflen, David Thompson,
Bijan Pesaran, and Partha P. Mitra. Comparing spectra and coherences
for groups of unequal size. J Neurosci Methods, 159:337–345, 2006.
[3] Hemant Bokil, Ofer Tchernichovski, and Partha P. Mitra. Dynamic
phenotypes: Time series analysis techniques for characterising neuronal
and behavioral dynamics. Neuroinformatics Special Issue on GenotypePhenotype Imaging in Neuroscience, 4:119–128, 2006.
[4] Michael S. Fee, Partha P. Mitra, and David Kleinfeld. Automatic sorting
of multiple unit neuronal signals in the presence of anisotropic and nongaussian variability. JOURNAL OF NEUROSCIENCE METHODS,
69:175–188, 1996.
[5] Rodolfo R. Llinas, Urs Ribary, Daniel Jeanmonod, Eugene Kronberg,
and Partha P. Mitra. Thalamocortical dysrhythmia: A neurological and
neuropsychiatric syndrome characterized by magnetoencephalography.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES
OF THE UNITED STATES OF AMERICA, 96:15222–15227, 1999.
[6] Clive Loader. Local Regression and Likelihood. Springer, 1999.
[7] Partha P. Mitra and Bijan Pesaran. Analysis of dynamic brain imaging
data. BIOPHYSICAL JOURNAL, 76:691–708, 1999.
[8] B Pesaran, JS Pezaris, M Sahani, PP Mitra, and RA Andersen. Temporal structure in neuronal activity during working memory in macaque
parietal cortex. NATURE NEUROSCIENCE, 5:805–811, 2002.
[9] O Tchernichovski, F Nottebohm, CE Ho, Bijan Pesaran, and PP Mitra.
A procedure for an automated measurement of song similarity. ANIMAL
BEHAVIOUR, 59:1167–1176, 2000.

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[10] Thilo Womelsdorf, Pascal Fries, Partha P. Mitra, and Robert Desimone.
Gamma-band synchronization in visual cortex predicts speed of change
detection. NATURE, 439:733–736, 2006.

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