STM32F10x DSP Library User Manual

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UM0585
User manual
STM32F10x
DSP library
Introduction
This user manual describes the STM32F10x DSP (digital signal processing) library, which is
a suite of common digital signal processing functions:
●

PID controller

●

Fast Fourier transform

●

FIR and IIR filters

The library contains C and assembly functions. The assembly code is ported on ARM®,
GCC and IAR Systems™ assemblers.

June 2010

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www.st.com

Contents

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Contents
1

DSP Library description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2

PID controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3

2.1

Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2

DSP library functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
DoPID function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.2

DoFullPID function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.3

PID_stm32 function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Complex 16-bit radix-4 FFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.1

Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2

DSP library functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.3

4

2.2.1

3.2.1

cr4_fft_64_stm32 function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2.2

cr4_fft_256_stm32 function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2.3

cr4_fft_1024_stm32 function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

FFT performance improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

16-bit FIR filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.1

Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.2

DSP library function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2.1

5

6

2/25

fir_16by16_stm32 function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

16-bit IIR filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
5.1

Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.2

DSP library functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
5.2.1

iiarma_stm32 function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5.2.2

iir_biquad_stm32 function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

STM32F10x DSP library benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
6.1

Function code footprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

6.2

Function execution time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
6.2.1

PID controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

6.2.2

Fast Fourier transform (FFT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

6.2.3

FIR filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
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Contents
6.2.4

IIR filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

7

STM32F10x DSP demo description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

8

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

9

Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

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List of tables

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List of tables
Table 1.
Table 2.
Table 3.
Table 4.
Table 5.
Table 6.
Table 7.
Table 8.
Table 9.
Table 10.
Table 11.
Table 12.
Table 13.
Table 14.
Table 15.
Table 16.
Table 17.
Table 18.
Table 19.

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STM32F10x DSP library functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
DoPID function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
DoFullPID function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
PID_stm32 function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
cr4_fft_64_stm32 function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
cr4_fft_256_stm32 function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
cr4_fft_1024_stm32 function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
fir_16by16_stm32 function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
iirarma_stm32 function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
iir_biquad_stm32 function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
STM32F10x DSP library functions code footprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
PID controller, error computed outside the routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
PID controller, error computed within the routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Complex radix 4, 16-bit FFT, coefficients in Flash memory . . . . . . . . . . . . . . . . . . . . . . . . 20
Complex radix 4, 16-bit FFT, coefficients in RAM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
16-bit, 32-tap FIR filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
16-bit canonic form, 4 biquad IIR filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
16-bit, 4th-order IIR filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Document revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

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List of figures

List of figures
Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.

Block diagram of PID controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Block diagram of an FIR filter of length N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Block diagram of the direct form I of second-order IIR filter . . . . . . . . . . . . . . . . . . . . . . . . 15
Block diagram of the canonical form of a second-order IIR filter . . . . . . . . . . . . . . . . . . . . 16
FFT of a sine wave with frequency f1 and of a dual sine wave with
frequencies f1 and f2, both sampled at a frequency Fs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

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DSP Library description

1

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DSP Library description
The STM32F10x DSPLib is a suite of common functions for signal processing. It includes
the following functions:
Table 1.

STM32F10x DSP library functions
Function name

6/25

Description

DoPID

PID controller in C, error computed outside the routine

DoFullPID

PID controller in C, error computed inside the routine

PID_stm32

PID controller in ASM, error computed outside the routine

cr4_fft_64_stm32

Complex radix-4 FFT for a 16-bit, 64-point vector

cr4_fft_256_stm32

Complex radix-4 FFT for a 16-bit, 256-point vector

cr4_fft_1024_stm32

Complex radix-4 FFT for a 16-bit, 1024-point vector

fir_16by16_stm32

16-bit FIR filter

iiarma_stm32

16-bit, 4th-order IIR filter

iir_biquad_stm32

16-bit, 8th-order, biquad IIR filter

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PID controller

2

PID controller

2.1

Description
The proportional-integral-derivative or PID controller is commonly used in the industry. It is a
feedback loop controller that manages the process command with a view to reducing the
error between the desired set point and the measured process variable.
The following block diagram shows the parallel structure of a PID controller. This is the
structure implemented in this DSP library.
Figure 1.

Block diagram of PID controller
P
Ref

Error

+-

I

+
+
+

command

Process

Output

In
D

ai15447

2.2

DSP library functions
The DSP library provides three PID functions:

2.2.1

●

DoPID: a PID core loop coded in C (the error is computed outside the function)

●

DoFullPID: a full PID controller coded in C (with error computing)

●

PID_stm32: an optimized PID core loop written in assembly

DoPID function
Table 2 describes the DoPID function.
Table 2.

DoPID function

Function name

DoPID

Prototype

uint16_t DoPID(uint16_t Error, uint16_t *Coeff)

Behavior description

PID in C, error computed outside the function.

Input parameter

– Error: difference between reference and measured values
– Coeff: pointer to the coefficients table

Output parameter

None

Return parameter

PID output command

Example
/* Fill the coefficients table */
Coeff[0] = Kp;/*proportional coefficient*/

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PID controller

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Coeff[1] = Ki;/*integral coefficient*/
Coeff[2] = Kd;/*derivative coefficient*/
/* Compute the error */
Error = Target_Signal - Measured_Signal;
/* PID control process */
Command = DoPID(Error, Coeff);

2.2.2

DoFullPID function
Table 3 describes the DoFullPID function.
Table 3.

DoFullPID function

Function name

DoFullPID

Prototype

uint16_t DoFullPID(uint16_t In, uint16_t Ref,
uint16_t *Coeff)

Behavior description

PID in C, error computed inside the function.

Input parameter

– In: Input (measured value)
– Ref: reference (target value)
– Coeff: pointer to the coefficients table

Output parameter

Computed error

Return parameter

PID output command

Example
/* Fill the coefficients table */
Coeff[0] = Kp;/*proportional coefficient*/
Coeff[1] = Ki;/*integral coefficient*/
Coeff[2] = Kd;/*derivative coefficient*/
/* PID control process, the error is computed inside the function */
Command = DoFullPID(Measured_Signal, Target_Signal, Coeff);

2.2.3

PID_stm32 function
Table 4 describes the PID_stm32 function.
Table 4.

PID_stm32 function

Function name

8/25

PID_stm32

Prototype

uint16_t PID_stm32(uint16_t Error, uint16_t *Coeff);

Behavior description

Assembly optimized PID controller with error computed outside the function.

Input parameter

– Error: difference between reference and measured values
– Coeff: pointer to the coefficients table

Output parameter

None

Return parameter

PID output command

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PID controller
The PID_stm32 function is used in the same way as the DoPID function. The error must be
computed, then the PID_stm32 function is called to improve the PID control process and to
return the appropriate command according to the coefficients table.

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Complex 16-bit radix-4 FFT

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3

Complex 16-bit radix-4 FFT

3.1

Description
The discrete Fourier transform (DFT) converts N complex values from the time domain to
the frequency domain.
The fast Fourier transform (FFT) is an optimized algorithm designed to compute the DFT
efficiently.
The STM32F10x DSP library provides a complex radix-4, with decimation-in-time, linearorder FFT.
Let x[N] be the time signal samples. To use the FFT functions of the DSP library, the
following conditions must be satisfied:

3.2

●

N is a power of 4

●

All the signal samples must be 32-bit data containing the 16-bit real part followed by the
16-bit imaginary part (in the little Endian order: imaginary_real).

DSP library functions
The DSP provides three complex 16-bit radix-4 FFT functions:

3.2.1

1.

cr4_fft_64_stm32: an optimized FFT function to compute 64-point DFT

2.

cr4_fft_256_stm32: an optimized FFT function to compute 256-point DFT

3.

cr4_fft_1024_stm32: an optimized FFT function to compute 1024-point DFT

cr4_fft_64_stm32 function
Table 5 describes the cr4_fft_stm32 function.
Table 5.

cr4_fft_64_stm32 function

Function name

10/25

cr4_fft_64_stm32

Prototype

void cr4_fft_64_stm32(void *pssOUT, void *pssIN,
uint16_t Nbin);

Behavior description

complex 16-bit, 64-point radix-4 FFT

Input parameter

– pssOUT: pointer to the output array data
– pssIN: pointer to the input array data
– Nbin: the number of points, must be 64.

Output parameter

None

Return parameter

None

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3.2.2

Complex 16-bit radix-4 FFT

cr4_fft_256_stm32 function
Table 6 describes the cr4_fft_256_stm32 function.
Table 6.

cr4_fft_256_stm32 function

Function name

3.2.3

cr4_fft_256_stm32

Prototype

void cr4_fft_256_stm32(void *pssOUT, void *pssIN,
uint16_t Nbin);

Behavior description

complex 16-bit, 256-point radix-4 FFT

Input parameter

– pssOUT: pointer to the output array data
– pssIN: pointer to the input array data
– Nbin: the number of points, must be 256.

Output parameter

None

Return parameter

None

cr4_fft_1024_stm32 function
Table 7 describes the cr4_fft_1024_stm32 function.
Table 7.

cr4_fft_1024_stm32 function

Function name

cr4_fft_1024_stm32

Prototype

void cr4_fft_1024_stm32(void *pssOUT, void *pssIN,
uint16_t Nbin);

Behavior description

complex 16-bit, 1024-point radix-4 FFT

Input parameter

– pssOUT: pointer to the output array data
– pssIN: pointer to the input array data
– Nbin: the number of points, must be 1024.

Output parameter

None

Return parameter

None

Example
#define N 64 /*Number of points*/
uint32_t x[N],y[N]; /* input and output arrays */
uint16_t real[N], imag[N]; /* real and imaginary arrays */
/* Fill the input array */
for(i=0; i= 8*/
/* Coefficients for the ARMA IIR filter */
short h2[5] = { 0x09c2, 0x270a, 0x3a8f, 0x270a, 0x09c2 };
short h1[5] = { 0x7fff, 0xd24a, 0x72ca, 0xcf4e, 0x1ad4 };
/* Input and output vectors */
short x[NY+4],y[NY+4];
/* Fill the input vector x */
...
/* Fill the 4 previous outputs */
y[0] = y0;
y[1] = y1;
y[2] = y2;
y[3] = y3;
/* Improve the filtering of NY samples */
iirarma_stm32(y, x, h2, h1, NY);

5.2.2

iir_biquad_stm32 function
Table 10 describes the iir_biquad_stm32 function.
Table 10.

iir_biquad_stm32 function

Function name

iir_biquad_stm32

Prototype

void iir_biquad_stm32(uint16_t *y, uint16_t *x, int16_t
*IIRCoeff, uint16_t ny)

Behavior description

8th-order 4 biquad IIR filter

Input parameter

–
–
–
–

Output parameter

None

Return parameter

None

y: output array
x: input array
IIRCoeff: IIR filter coefficients
ny: number of output samples

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16-bit IIR filters

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Example
#define NY 32/*number of outputs*/
/* Coefficients for the biquad IIR filter: 4 sections, with 5
coefficients in each section */
int16_t Coeff[20] = {...};
/* Input and output vectors */
short x[NY],y[NY];
/* Fill the input vector x */
...
/* Improve the filtering of NY samples */
iir_biquad_stm32(y, x, Coeff, NY);

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6

STM32F10x DSP library benchmark

STM32F10x DSP library benchmark
This section provides the STM32F10x DSP library benchmark results, which are computed
using the IAR EWARM 5.20 toolchain, with high-speed optimization.

6.1

Function code footprint
Table 11.

STM32F10x DSP library functions code footprint
Function name

Code size (bytes)

DoPID

52

DoFullPID

58

PID_stm32

72

cr4_fft_64_stm32

718(1)

cr4_fft_256_stm32

1486(1)

cr4_fft_1024_stm32

4560(1)

fir_16by16_stm32

162

iiarma_stm32

156

iir_biquad_stm32

294

1. FFT code size was computed with FFT coefficients table stored in Flash memory. If the FFT coefficients
are stored in SRAM, the code size of the three FFT functions is equal to 480 bytes.

6.2

Function execution time

6.2.1

PID controller
Table 12.

PID controller, error computed outside the routine

PID

24 MHz
0 wait state

48 MHz
1 wait state

72 MHz
2 wait states

cycle count

time

cycle count

time

cycle count

time

ASM function

45

1.87 µs

51

1.06 µs

59

0.819 µs

C function

47

1.96 µs

50

1.04 µs

54

0.75 µs

Analysis of the PID timing shows that assembly code is not as fast as C code. The compiler
is more efficient in accessing variables than manual optimization (offset computation and
data placement in literal pool).

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STM32F10x DSP library benchmark
Table 13.

PID controller, error computed within the routine
24 MHz
0 wait state

PID

C function

6.2.2

72 MHz
2 wait states

cycle count

time

cycle count

time

cycle count

time

48

2 µs

52

1.08 µs

57

0.79 µs

Complex radix 4, 16-bit FFT, coefficients in Flash memory

FFT
(ASM funct.)

24 MHz
0 wait state

48 MHz
1 wait state

72 MHz
2 wait states

cycle count

time

cycle count

time

cycle count

time

64 points

3847

0.16 ms

4 472

0.093 ms

5 661

0.078 ms

256 points

21 039

0.876 ms

24 964

0.52 ms

31 527

0.437 ms

1024 points

100 180

4.174 ms

114 350

2.382 ms

153 930

2.138 ms

Table 15.

Complex radix 4, 16-bit FFT, coefficients in RAM

FFT
(ASM funct.)

24 MHz
0 wait state

48 MHz
1 wait state

72 MHz
2 wait states

cycle count

time

cycle count

time

cycle count

time

64 points

3 847

0.16 ms

4 025

0.084 ms

4 764

0.066 ms

256 points

21 039

0.876 ms

22 176

0.462 ms

26 065

0.362 ms

1024 points

100 180

4.174 ms

102 057

2.126 ms

127 318

1.768 ms

FIR filter
Table 16.

16-bit, 32-tap FIR filter

FIR
(ASM filter)
32 samples

20/25

48 MHz
1 wait state

Fast Fourier transform (FFT)
Table 14.

6.2.3

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24 MHz
0 wait state

48 MHz
1 wait state

72 MHz
2 wait states

cycle count

time

cycle count

time

cycle count

time

3516

146.5 µs

3525

73.4 µs

3727

51.76 µs

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6.2.4

STM32F10x DSP library benchmark

IIR filters
Table 17.

16-bit canonic form, 4 biquad IIR filter
24 MHz
0 wait state

IIR
(C filter)
32 samples

Table 18.

72 MHz
2 wait states

cycle count

time

cycle count

time

cycle count

time

3478

144.9 µs

3636

75.75 µs

3929

54.57 µs

16-bit, 4th-order IIR filter

IIR
(ASM filter)
32 samples

48 MHz
1 wait state

24 MHz
0 wait state

48 MHz
1 wait state

72 MHz
2 wait states

cycle count

time

cycle count

time

cycle count

time

1696

70 µs

1761

36.69 µs

1986

27.58 µs

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STM32F10x DSP demo description

7

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STM32F10x DSP demo description
The STM32F10x DSP demo is an example that illustrates how to use the 64-point FFT
function of the STM32F10x DSP library. It consists of an LCD that displays the FFT
transformation.
The demo runs on the STM3210B-EVAL board, and shows the 64-point FFT transformation
of two signals:
1.

a sine wave

2.

a dual sine wave

The two types of wave are displayed at variable frequencies and for each frequency the FFT
is computed and the result is plotted as shown in Figure 5:
●

The frequency (f1) of the sine wave is increased from 40 Hz to 4 kHz by steps of 30 Hz.

●

The dual sine wave is the sum of a constant-frequency (f2) sine wave and the above
described variable-frequency (f1) sine wave.

Figure 5.

FFT of a sine wave with frequency f1 and of a dual sine wave with
frequencies f1 and f2, both sampled at a frequency Fs
Sine wave

–Fs
2

–f1

f1

Fs
2

Dual sine wave

–Fs –f2 –f1
2

f1

f2

Fs
2

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8

Conclusion

Conclusion
This user manual describes the STM32F10x DSP library, which contains:
●

a PID controller

●

complex 16-bit radix-4 FFT optimized functions for 64, 256 and 1024 points

●

a 16-bit FIR filter

●

a 16-bit direct-form I IIR filter

●

a 16-bit canonical-form IIR filter designed by biquads

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Revision history

9

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Revision history
Table 19.

Document revision history

Date

Revision

13-Oct-2008

1

Initial release.

2

Introduction modified.
Table 1: STM32F10x DSP library functions updated.
Section 7: STM32F10x DSP demo description added.
u32 changed to uint32_t.
u16 changed to uint16_t.
s16 changed to int16_t.
Small text changes.

04-Jun-2010

24/25

Changes

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