Transcript Finite Impulse Filters - FIR

DSP C5000
Chapter 14
Finite Impulse Response (FIR)
Filter Implementation
Copyright © 2003 Texas Instruments. All rights reserved.
Outline
Digital Filters and FIR filters
Implementation of FIR Filters on C54x
Implementation of FIR Filters on C55x
Comparison of C54x and C55x
ESIEE, Slide 2
Copyright © 2003 Texas Instruments. All rights reserved.
Outline of FIR Filters



ESIEE, Slide 3
Generalities on Digital Filters
FIR Filters with Matlab
Implementation of FIR Filters
Copyright © 2003 Texas Instruments. All rights reserved.
Digital Filters
Sampling
frequency
fS
x(t)
Analog
antialiasing
filter
yn
xn
A
D
C
Digital Filter
xn
D
A
C
Analog
y(t)
smoothing
filter
yn
Digital Filter
ESIEE, Slide 4
Copyright © 2003 Texas Instruments. All rights reserved.
Linear, Time-Invariant Digital Systems

 1 R

2  R
Linearity
1x1( n)  2 x2 ( n)  1 y1( n)  2 y2 ( n)

Time Invariance
x( n )  y( n)  x( n  n0 )  y( n  n0 )
ESIEE, Slide 5
Copyright © 2003 Texas Instruments. All rights reserved.
Impulse Response
n  0 un  0

Impulse sequence un 
u0  1
n  0 u  0
n

un
n=0
ESIEE, Slide 6
Digital Filter
hn
Copyright © 2003 Texas Instruments. All rights reserved.
Input-Output Relationship, Convolution
xn
n=-1 0
1
2
=
n=-1 0
1
2
+
n=-1 0
1
2
+
n=-1 0
1
2
+
n=-1 0
1
2
x-1un+1
xn 

xu
k 
k nk
x0un
x1un-1
x2un-2
ESIEE, Slide 7
Copyright © 2003 Texas Instruments. All rights reserved.
Input-Output Relationship, Convolution

yn 
Using linearity and time invariance:
k 
 x output(u
k 
yn 
ESIEE, Slide 8
k
nk
)
k 
xh
k 
k 
k 
k 
k 
k nk
 xk hnk   hk xnk
Copyright © 2003 Texas Instruments. All rights reserved.
Output for a Single Frequency Input

Single frequency input  Single frequency output
xn  e
j0nTe
yn  xn H (0 )
H (0 ) 
H(0 )  H(0 ) e
ESIEE, Slide 9
k 
 hk e
 j0kTe
k 
j arg( H (0 ))
 A(0 )e
j(0 )
Copyright © 2003 Texas Instruments. All rights reserved.
Frequency Transfer Function

For a digital filter the frequency
transfer function is periodic.
H( )  H( ) e
1
hn 
2f e
f e
 H ( )e
j arg( H ( ))
jnTe
ESIEE, Slide 10
Amplitude
d
f e
( )  arg H 
Phase
 A( )e
j( )
( )
 ( )  

Group
delay
Copyright © 2003 Texas Instruments. All rights reserved.
Relationship Between Fourier Transforms
of Input and Output
X ( ) 
n
 xn e
n
 jnTe
Y ( ) 
n
 yn e
 jnTe
n
Y ( )  H ( ) X ( )
ESIEE, Slide 11
Copyright © 2003 Texas Instruments. All rights reserved.
Z Transfer Function
H( z) 

 hn z
n
n
H ( ) 

 hne
n
 jnTe
 H ( z ) z e jTe
Y( z )  X ( z )H( z )
ESIEE, Slide 12
Copyright © 2003 Texas Instruments. All rights reserved.
Basic Relationships of a Digital Filter
yn 
k 
k 
k 
k 
 xk hnk   hk xnk
Y ( )  H ( ) X ( )
Y( z )  X ( z )H( z )
ESIEE, Slide 13
Copyright © 2003 Texas Instruments. All rights reserved.
Rational z Transfer Function
Q
N(z)
H(z) 

D( z )
 bi z
i0
P
i
1   ak z
k
k 1

Linear equation with constant coefficients.
Q
P
i 0
k 1
yn   bi xni   ak ynk
ESIEE, Slide 14
Copyright © 2003 Texas Instruments. All rights reserved.
IIR and FIR Filters


IIR = Infinite Impulse Response
FIR = Finite Impulse Response

Q
H ( z )   bi z 
i0
i

FIR
 hn z
n 

n
 n  0, Q  1 hn  0

n  0, Q  1 hn  bn
IIR
N(z)
With D( z)  constant.
H(z) 
D( z )
ESIEE, Slide 15
Copyright © 2003 Texas Instruments. All rights reserved.
FIR and IIR

FIR: output yn is a linear combination of a
finite number of input samples.
Q
Q
i 0
i 0
yn   hi xni   bi xni , bi  hi .

IIR: output yn is a linear combination of a
finite number of input and of output
samples. Recursive form.
Q
P
i 0
k 1
yn   bi xni   ak ynk
ESIEE, Slide 16
Copyright © 2003 Texas Instruments. All rights reserved.
Causality and Stability



A filter is causal if hn=0 for n < 0
A filter is stable if the output is bounded
for any bounded input.
Condition for stability is:

All the poles of H(z) are inside the unit circle


FIR are always stable.
Or:

 hn
A
n
ESIEE, Slide 17
Copyright © 2003 Texas Instruments. All rights reserved.
Representation of Poles and Zeroes of H(z) in
the Complex Plane
Imaginary Part
1
0.5
Real Part
0
-0.5
-1
-1
ESIEE, Slide 18
-0.5
0
0.5
1
Copyright © 2003 Texas Instruments. All rights reserved.
Some Useful Matlab Functions

Example for a FIR filter:
N ( z )  b0  b1 z
b  [b0

 b3 z
3
b2 ]  [1 1 1 1].
b=[1 1 1 1]; a=1;
Calculate transfer function Hf, its
amplitude and phase on 256 samples,
with fs=1:



ESIEE, Slide 19
b2
 b2 z
2
Enter the filter coefficients vector b:


b1
1
[Hf,f]=freqz(b,a,256,1);
HfA=abs(Hf);
Hfphi=angle(Hf);
Copyright © 2003 Texas Instruments. All rights reserved.
Some Useful Matlab Functions
Plot impulse response: stem(b)
Plot amplitude and phase of transfer
function: plot(f,HfA) and plot(f,Hfphi)


Phase of the transfer function
1
Amplitude of the transfer function
4
3.5
0.5
3
0
2.5
-0.5
2
-1
1.5
-1.5
1
-2
0.5
-2.5
0
ESIEE, Slide 20
0.05
0.1
0.15
0.2
0.3
0.35
0.25
Frequency, FS=1
0.4
0.45
0.5
0
0
0.05
0.1
0.15
0.2
0.3
0.35
0.25
Frequency, FS=1
0.4
0.45
0.5
Copyright © 2003 Texas Instruments. All rights reserved.
Some Useful Matlab Functions

Generate a test signal = sum of cosines:


Apply the filter to x. Output is y:


x=cos(2*pi*[0:99]*0.25)+2*cos(2*pi*[0:99]*0.1);
y=filter(b,a,x);
Plot the results: plot(x); plot(y)
Input x
3
x is the sum of
2 frequencies :
0.25 and 0.1.
2
4
1
2
0
0
-1
-2
-2
-4
-3
ESIEE, Slide 21
0
20
40
Time
60
Output y
6
80
100
-6
The filter
cancels the
frequency 0.25.
y has only the
freq. 0.1.
0
20
40
60
80
100
Time
Copyright © 2003 Texas Instruments. All rights reserved.
Calculation of a FIR using Matlab

For given attenuation and frequency
response characteristics, the transfer
function can be calculated using
different methods:



Corresponding Matlab functions


ESIEE, Slide 22
Mean square error, miniMax (Chebychev)
Empirical window method
firls and remez.
fir and fir1.
Copyright © 2003 Texas Instruments. All rights reserved.
Example using Matlab

Design a low pass filter:




Sampling frequency = 9600 Hz
Maximum attenuation (passband) = 0.1 dB
Minimum attenuation (stopband) = 50 dB
Limit frequencies of passband and
stopband = 1200 Hz and 2600 Hz.
Attenuation in dB
f in Hz
1200
ESIEE, Slide 23
2600
Copyright © 2003 Texas Instruments. All rights reserved.
Example using Matlab





ESIEE, Slide 24
Vector of limited frequencies (normalized)
 F=[0 1200 2600 4800]/4800;
Vector of required amplitudes:
 A=[1 1 0 0];
Least square calculation of filter:
 Bls=firls(23,F,A);
Mini Max calculation of filter:
 Bre=remez(21,F,A);
Window method (Hamming):
 Bwin=fir1(25,(1200+2600)/9600);
Copyright © 2003 Texas Instruments. All rights reserved.
Results of Matlab Example

The minimum orders to satisfy the
constraints are 23 for LS, 21 for
minimax and 25 for the window method.
140
Least square
method
120
Attenation in dB =
20*log(1/|H(f)|)
100
Window
method
80
60
40
20
Mini Max
window
0
Frequency
-2 0
0
ESIEE, Slide 25
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Copyright © 2003 Texas Instruments. All rights reserved.
Results of Matlab Example
Impulse Response

0.4
0.35
hn
0.3
0.25
0.2
0.15
0.1
0.05
n
0
-0.05
-0.1
ESIEE, Slide 26
0
5
10
15
20
25
Copyright © 2003 Texas Instruments. All rights reserved.
FIR Filters with Constant Group Delay or
Linear Phase

For many applications, it is desirable to
use a filter with a constant group delay
(independant of the frequency).


2 possible cases:




ESIEE, Slide 27
The phase will be linear or affine.
symmetrical or asymmetrical FIR.
Constant group delay = TS (N-1)/2
Symmetrical:
h(n)=h(N-1-n)
Asymmetrical;
h(n)=-h(N-1-n)
Copyright © 2003 Texas Instruments. All rights reserved.
FIR filters with Constant Group Delay or
Linear Phase

Asymmetric case: linear phase
( f )  kf

Asymmetrical case:
( f )  kf 
ESIEE, Slide 28

2
Copyright © 2003 Texas Instruments. All rights reserved.
Fixed Point Implementation of FIR Filters
Numerical Issues

Fixed point implementation:



Fixed point representation of data


16 bits for data and coefficients
Accumulators have size 40 bits
Size B = 16 bits, Format Qk: k fractional bits
Quantization of coefficients


Maximum magnitude coefficient = hmax
Number of bits of the integer part of
coefficients is Bi:


ESIEE, Slide 29
Bi = log2(hmax)
Coefficients in Qk’ with k = 16-Bi
Copyright © 2003 Texas Instruments. All rights reserved.
Matlab Example

The coefficients Bre can be quantized
using 16-bit fixed point with 15 fractional
bits:


To store the result in a text file for CCS:





ESIEE, Slide 30
Bre=round(Bre*2^15);
fp=fopen('coef.asm','wt')
for i=1:22
fprintf(fp,' .word %d \n',Ba(i))
end
fclose(fp)
Copyright © 2003 Texas Instruments. All rights reserved.
Matlab Example


ESIEE, Slide 31
File coef.asm
Can be edited
to be used
with CCS.
.word
.word
.word
.word
.word
.word
.word
.word
.word
.word
.word
.word
.word
.word
.word
.word
.word
.word
.word
.word
.word
.word
39
-92
-242
25
668
579
-978
-2229
86
6374
12127
12127
6374
86
-2229
-978
579
668
25
-242
-92
39
Copyright © 2003 Texas Instruments. All rights reserved.
FIR Implementation, Numerical issues,
FRCT bit

Common case:




ESIEE, Slide 32
Data and coefficients in Q15 format
Product h(i)x(n-i) in Q30 (2 sign bits)
By shifting products 1 bit left, the product
are in Q31 format with only 1 sign bit.
If the FRCT bit (Fraction) is set to 1,
products are automatically shifted 1 bit
left.
Copyright © 2003 Texas Instruments. All rights reserved.
Structures for FIR Implementation

Common structures for FIR filters


Transversal structures
Trellis structure


Transversal structures using:



ESIEE, Slide 33
Useful in some adaptive situations.
Linear buffers
Circular buffers
Special case for symmetrical or
asymmetrical FIRs.
Copyright © 2003 Texas Instruments. All rights reserved.
Transversal Structures of FIR
Structure with a delay line

xn-1
xn
b0
b1
xn-2
b2
xn-N+1
b3
bN-1
yn

Transposed structure
yn
bN-1
bN-2
b3
b2
b1
b0
xn
ESIEE, Slide 34
Copyright © 2003 Texas Instruments. All rights reserved.
Implementation of a FIR with a Delay Line

Most common structure used in DSP.


The delay line can be implemented using a
linear or a circular buffer.
Basic operations:



Read a new data value x(n) every TS
ACCU=0
for i=0 to N-1:


ESIEE, Slide 35
Multiply h(i) by x(n-i) and add it to
accumulator
Output y(n)
Copyright © 2003 Texas Instruments. All rights reserved.
Implementation of FIR Filters on C54x

Implementation of General
Transversal FIR filters



ESIEE, Slide 36
Using linear buffers
Using circular buffers
Implementation of Symmetrical
FIR filters
Copyright © 2003 Texas Instruments. All rights reserved.
Operations using a Linear Buffer for a FIR
with N Coefficients




Length of the delay line = N samples
Read a new sample x(n) and store it in the
delay line in the first position.
ACCU=0
for i=0 to N-1




ESIEE, Slide 37
Read h(i) and x(n-i)
Multiply h(i) by x(n-i) and add it to ACCU
Output y(n)
N-1 Shifts in the delay line.
Copyright © 2003 Texas Instruments. All rights reserved.
Linear Buffer, MACD Mode




Instead of shifting N-1 samples at the
end, do the shift in the loop one by one.
Read a new sample xn and store it in the
delay line in the first position.
ACCU=0
for i=N-1 to 0




ESIEE, Slide 38
Read h(i) and x(n-i)
Multiply h(i) by x(n-i) and add it to ACCU
Shift x(n-i) in the delay line
Output y(n)
Copyright © 2003 Texas Instruments. All rights reserved.
MACD Instruction

MACD:


Multiply Accumulate and Delay move.
MACD Smem, pmad, src




If MACD used in a loop with RPT the
program memory (pmad) address is
automatically incremented.


ESIEE, Slide 39
src=src+Smem*pmad;
T=Smem;
(Smem+1)=Smem
MACD alone = 3 cycle times
In a RPT loop 1 cycle time
Copyright © 2003 Texas Instruments. All rights reserved.
Implementing a FIR with MACD

Memory organization of data and coefficients
Program Memory
Addresses
Content
i=pmad
b(N-1)
i+1
b(N-2)
i+2
b(N-3)
…
…
i+N-1
b(0)
Data Memory
Addresses
Content
k=Smem
x(n)
k+1
x(n-1)
k+2
x(n-2)
…
k+N-1
x(n-N+1)
dummy place
for copy of
k+N
ESIEE, Slide 40
x(n-N+1)
Copyright © 2003 Texas Instruments. All rights reserved.
Initialization of Registers

STM Stores #value to the MMR early
in the pipeline to avoid latencies.


Initialization of FRCT bit (fractional
mode):


Instructions SSBX (Set Status Bit) and
RSBX (Reset Status Bit).
Initialization of ACCU


ESIEE, Slide 41
2 words, 2cycles.
Using RPTZ :RePeaT after initializing
ACCU at 0
Or via LD #0,A
Copyright © 2003 Texas Instruments. All rights reserved.
RPT, RPTZ Instructions

RPT #n



RPTZ src, #n



ESIEE, Slide 42
Repeat next instruction n+1 times.
Repetition counter set to n and decreases
until 0.
1 or 2 cycles, not interruptible.
Same as repeat, except that src ACCU is
cleared to zero before repeat.
2 cycles , not interruptible.
Some instructions execute faster when
in repeat mode (pipeline).
Copyright © 2003 Texas Instruments. All rights reserved.
Implementing a FIR Filter with MACD
.bss
adr_fin_dat .set
.text
* Initialization of
STM
SSBX
* Filter loop
RPTZ
MACD

adr_debut_dat,N+1
adr_debut_dat+N-1
AR1 and FRCT
#adr_fin_dat, AR1
FRCT
A, #N-1
*AR1-, adr_coef, A
Test with CCS


ESIEE, Slide 43
Filter with N=32 coefficients all equal to 1/32
Create a file fircoef.asm, address of coefficients in
program mem = adr_coef
Copyright © 2003 Texas Instruments. All rights reserved.
Implementing a FIR Filter with MACD

File containing coefficients fircoef.asm
adr_coef
ESIEE, Slide 44
.global
adr_coef
.sect ".coef"
.word 0X400, 0X400
.word 0X400,0X400,0X400,0X400,0X400
.word 0X400,0X400,0X400,0X400,0X400
.word 0X400,0X400,0X400,0X400,0X400
.word 0X400,0X400,0X400,0X400,0X400
.word 0X400,0X400,0X400,0X400,0X400
.word 0X400,0X400,0X400,0X400,0X400
Copyright © 2003 Texas Instruments. All rights reserved.
Implementing a FIR Filter with MACD

File firmacd.asm with the program

2 files to compile and link:


Test by associating files on the ports
DRR0 and DXR0


ESIEE, Slide 45
fircoef.asm and firmacd.asm
File infir.dat attached to DRR0
File outfir.dat attached to DXR0
Copyright © 2003 Texas Instruments. All rights reserved.
Implementing a FIR Filter with MACD

Program file firmacd.asm: initializations
N
adr_fin_dat
.mmregs
.global
.global
.global
.set
.bss
.set
.text
* Initialization of
LD
SSBX
* Initialization of
STM
STM
STM
ESIEE, Slide 46
adr_debut_dat
adr_fin_dat
adr_coef
32
adr_debut_dat,N+1
adr_debut_dat+N-1
DP and FRCT
#0, DP
FRCT
AR0, AR1, AR2
#(adr_debut_dat),AR2
#(adr_debut_dat-1),AR1
#N, AR0
Copyright © 2003 Texas Instruments. All rights reserved.
Implementing a FIR Filter with MACD

Program file firmacd.asm: endless loop
debut:
* set AR1 at adr_fin_dat
MAR
*AR1+0
* Read x(n) at DRR
LDM
DRR0, A
STL
A,*AR2
* Endless filter loop
RPTZ
A, #N-1
MACD
*AR1-, adr_coef, A
* Write y(n) in DXR
* by saving the high part of ACCU in DXR
STH
A,DXR0
* Go back to the beginning of the loop
B
debut
ESIEE, Slide 47
See files
firmacd.asm
and
fircoef.asm
for the test in
directory
tutorial.
Copyright © 2003 Texas Instruments. All rights reserved.
FIR with MACD, Test with CCS


Create project, create command file,
compile and link.
To test the impulse response:

Create a file infir.dat with:


Set 2 probe points



1 at reading of DRR: LDM DRR
1 at end of loop: B debut
Attach files to probe points


ESIEE, Slide 48
A value 0.5 (0x4000) then zeros (at least 40)
infir.dat at 1rst probe point (read value stored
at address 0x20 DRR)
outfir.dat at second probe point (data at
address 0x21 DXR is strored in the file)
Copyright © 2003 Texas Instruments. All rights reserved.
Results



Let program run until end of file
infir.dat
Load file outfir.dat at some address in
the DSP data memory (File-Data-Load)
Plot the content of this memory area
(View-Graph-Time/Frequency).


ESIEE, Slide 49
Plot a time graph (Single Time)
Plot a frequency graph (FFT: Magnitude
and Phase)
Copyright © 2003 Texas Instruments. All rights reserved.
Results for the impulse response and its FFT
ESIEE, Slide 50
Copyright © 2003 Texas Instruments. All rights reserved.
Second Test




ESIEE, Slide 51
New test with a sine input.
Replace infir.dat by file insinus.dat
containing 80 samples of a sine with 40
samples per period of sine.
Name outsine.dat the result file.
Repeat the same operations as in the
preceding test.
Copyright © 2003 Texas Instruments. All rights reserved.
Second test

ESIEE, Slide 52
Observe that the output is attenuated and is phase
shifted by values corresponding at H(f) at fS/40.
Copyright © 2003 Texas Instruments. All rights reserved.
Implementation using a Circular Buffer

A circular buffer of length N is a block
of contiguous memory words addressed
by a pointer using a modulo N
addressing mode.


Characteristics of a circular buffer:


ESIEE, Slide 53
The 2 extreme words of the memory block
are considered as contiguous.
Instead of moving the N data in memory,
just modify the pointers.
When a new data x(n) arrives, the pointer
is incremented and the new data is written
in place of the oldest one.
Copyright © 2003 Texas Instruments. All rights reserved.
Trace of Memory and Pointer in a Circular
Buffer of Length 3
ESIEE, Slide 54
Time n
Time n+1
Time n+2
Time n+3
x(n-1)
x(n)
x(n-2)
x(n-1)
x(n)
x(n+1)
x(n+2)
x(n)
x(n+1)
x(n+2)
x(n+3)
x(n+1)
Copyright © 2003 Texas Instruments. All rights reserved.
FIR with Circular Buffers

2 circular buffers


1 for data
1 for coefficients
Data
Memory
adr_deb_data
Coefficient
memory
adr_deb_coef
b(N-1)
b(N-2)
pnt_coef
pnt_data
adr_fin_coef
ESIEE, Slide 55
adr_fin_coef
b(0)
Copyright © 2003 Texas Instruments. All rights reserved.
Operation of FIR with Circular Buffer




Read a new input sample x(n)
Store it at address of pnt_data
ACCU=0
for i=1 to N-1





ESIEE, Slide 56
multiply data pointed by pnt_data by
coefficient pointed by pnt_coef. Add
product to ACCU
decrement pointers pnt_data and pnt_coef
end
output y(n) from ACCU
increment pnt_data of 1
Copyright © 2003 Texas Instruments. All rights reserved.
Instruction MAC with 2 operands in Indirect
Addressing Mode

MAC: Multiply and Accumulate

MAC Xmem, Ymem, src[, dest]





Dual operand instructions indirect
addressing restricted to:


ESIEE, Slide 57
dst=src+Xmem*Ymem
T=Xmem
With Xmem, Ymem use only AR2 to AR5
Can be executed in 1 cycle time.
AR2, AR3, AR4, AR5
none, +, -, +0%
Copyright © 2003 Texas Instruments. All rights reserved.
Circular Buffer with C54x

Circular indirect addressing mode:


*ARi-%, *ARi+%, *ARi-0%, *ARi+0%,
*ARi(lk)%
In dual operand mode Xmem, Ymem:



BK register:



ESIEE, Slide 58
*ARi+0% only valid mode
To perform a decrement, store a negative value
in AR0.
Stores the size N of the circular buffer.
Must be initialized before use.
There may be several circular buffers at
different addresses at the same time but
with the same length.
Copyright © 2003 Texas Instruments. All rights reserved.
Limitations on Start Addresses of Circular
Buffers

If N is written on nb bits in binary, the
start address must have its nb LSB at 0:

Examples:



To access a circular buffer:


Initialize BK with N (nb bits)
Choose 1 ARi as a pointer


ESIEE, Slide 59
for N=32, 6 LSB of start address =0
for N=30, 5 LSB of start address =0
The effective start address of the buffer is the
value in ARi with its nb LSB at 0.
The end address = start addess +N-1.
Copyright © 2003 Texas Instruments. All rights reserved.
Circular buffer on C54x
Data Memory
Start_address =
xxxxxxxxxxx00000
ARi
BK
xxxxxxxxxxx00010
N=30=1 1 1 1 0
ARi
End_address =
xxxxxxxxxxx11111
ESIEE, Slide 60
Copyright © 2003 Texas Instruments. All rights reserved.
Implementation of FIR Filter
with 2 Circular Buffers



Same filter as in the preceding example,
coefficients in section .coef (in program
memory) in file fircoef.asm.
N=32
2 buffers are allocated in data memory
for the coefficients and the data of the
filters


First step of program after initialization:

ESIEE, Slide 61
Start addresses must be multiple of 64.
Transfer coefficients from program to data
memory from adr_coef to adr_debut_coef.
Copyright © 2003 Texas Instruments. All rights reserved.
Move Instructions

MVPD #pmad, Smem


Copy values from program to data memory
In RPT mode pmad is automatically
incremented.
Program
Data
MVPD, MVDP
READA, WRITEA
Data
Data
MVKD, MVDK, MVDD
ESIEE, Slide 62
MMR
Data
MVMD, MVDM
MMR
MMR
MVMM
Copyright © 2003 Texas Instruments. All rights reserved.
Implementation of FIR with 2 Circular
Buffers, Initializations
N
adr_debut_dat
adr_debut_coef
adr_fin_dat
adr_fin_coef
.mmregs
.global
.global
.global
.global
.global
adr_debut_dat
adr_fin_dat
adr_debut_coef
adr_fin_coef
adr_coef
.set
.usect
.usect
.set
.set
32
"buf_data", N
"buf_coef", N
adr_debut_dat+N-1
adr_debut_coef+N-1
.text
* Initialization of BK,AR0,FRCT
STM
#N, BK
STM
#-1, AR0
SSBX
FRCT
* Initialization of AR2, AR3
STM
#(adr_debut_dat),AR2
STM
#(adr_fin_coef),AR3
ESIEE, Slide 63
Copyright © 2003 Texas Instruments. All rights reserved.
Implementation of FIR with 2 Circular
Buffers, Program
* Transfer of coefficients from
* program to data memory
STM
#adr_debut_coef, AR4
RPT
#N-1
MVPD
adr_coef, *AR4+
* Endless loop
debut:
* Read x(n) at DRR
LDM
DRR0, A
STL
A, *AR2
* Calculation of y(n)
RPTZ
A, #N-1
MAC
*AR2+0%, *AR3+0%, A
* Write y(n) in DXR
* by saving high part of ACCU
STH
A, DXR0
* Go back to the beginning of the loop
MAR
*AR2+
B
debut
ESIEE, Slide 64
See files
fircirc.asm
and
fircoef.asm
for the test.
Copyright © 2003 Texas Instruments. All rights reserved.
Command File for Circular Buffer
Addressing Constraint

The addresses adr_debut_dat and
adr_debut_coef have to be aligned with
a multiple of 64 in the example.



adr_debut_dat is the start address of
unitialized section buf_data.
adr_debut_coef is the start address of
unitialized section buf_coef.
To align the 2 sections on a multiple of 64,
in the command file add align(64) after the
name of the sections in the MEMORY
directive, for example:

ESIEE, Slide 65
buf_data align(64) > DATA
page 1
Copyright © 2003 Texas Instruments. All rights reserved.
Implementation of a Symmetrical FIR filter

The symmetry of coefficients is used to decrease the
computational load:
 b(n)=b(N-1-n)
 N time cycles for a general FIR filter with N
coefficients is N (in good conditions).
 N/2 time cycles for a symmetrical FIR filter.
 Use of specific instruction FIRS.
N
1
2
y (n)   b(i)  x(n  i )  x(n  N  1  i )  N even
i 0
N 1
1
2
N 1 
 N 1  
y (n)   b(i)  x(n  i )  x(n  N  1  i )   b 
x
n

 
 N odd
2 
 2  
i 0
ESIEE, Slide 66
Copyright © 2003 Texas Instruments. All rights reserved.
FIRS Instruction to Work with RPT(Z)


FIRS Xmem, Ymem, pmad
Xmem, Ymem corresponds to:



x(n-i), x(n-N+1+i)
Coefficients in program memory pmad
operations of FIRS:


pmad PAR
while RC  0




ESIEE, Slide 67
B = B + A(32:16) x Pmem addressed by PAR
A = (Xmem+Ymem)<<16
PAR=PAR+1
RC=RC-1
Copyright © 2003 Texas Instruments. All rights reserved.
Using FIRS for a Symmetrical FIR Filter

3 arrays:


N/2 first coefficients,
N/2 newest data and N/2 oldest data.
adr_debut_coef
PAR
Program
Memory
Data
Memory
b(0)
x(n-2)
b(1)
b(2)
x(n)
x(n-1)
x(n-3)
adr_debut_dat0
AR2
adr_debut_dat1
AR3
x(n-5)
x(n-4)
Example for N = 6
2 circular
buffers
ESIEE, Slide 68
Copyright © 2003 Texas Instruments. All rights reserved.
Using FIRS for a Symmetrical FIR Filter


BK = N/2
At the beginning AR2 and AR3 point to:


the newest data x(n)
and the oldest data x(n-N+1)
Beginning
x(n)
x(n-1)
x(n-N/2-1)
ESIEE, Slide 69
x(n-N+3)
x(n-N/2)
x(n-N+1)
x(n-N+2)
After N/2 +1 incrementations
x(n)
x(n-1)
x(n-N/2-1)
x(n-N+3)
x(n-N/2)
x(n-N+1)
x(n-N+2)
Copyright © 2003 Texas Instruments. All rights reserved.
Using FIRS for a Symmetrical FIR Filter



FIRS is repeated N/2 times
The first sum x(n)+x(n-N+1) is done
before entering the loop.
N/2 iterations (AR2 and AR3 incremented
by 1):




ESIEE, Slide 70
At the first iteration AR2 points on x(n-1) and
AR3 on x(n-N+2)
After N/2 iterations: AR2 is decremented of 2
and AR3 of 1.
The oldest sample x(n-N/2+1) of 1st buffer is
stored in 2nd buffer in place of x(n-N+1).
Then AR is incremented by 1.
New sample x(n+1) is stored in place of x(n).
Copyright © 2003 Texas Instruments. All rights reserved.
Symmetrical FIR Implementation with FIRS,
Initializations
N
Nsur2
adr_debut_coef
adr_debut_dat
adr_debut_dat1
.mmregs
.global
.global
.global
.set
.set
.set
.usect
.usect
adr_debut_coef
adr_debut_dat0
adr_debut_dat1
32
16
adr_coef
"buf_data0", N
"buf_data1", N
.text
* Initialization of BK, AR0,FRCT
STM
#Nsur2, BK
STM
#-2, AR0
SSBX
FRCT
* Initialization of AR2, AR3
STM
#(adr_debut_dat0),AR2
STM
#(adr_debut_dat1),AR3
ESIEE, Slide 71
Copyright © 2003 Texas Instruments. All rights reserved.
Symmetrical FIR Implementation using
FIRS, Program
* Endless loop
debut:
* Read x(n) at DRR
LDM
DRR0, A
STL
A, *AR2
* Calculation of y(n)
* Calculation of the first sum
ADD
*AR2+0%,*AR3+0%,A
* Repeat N/2 times FIRS
RPTZ
B, #(Nsur2-1)
FIRS
*AR2+0%, *AR3+0%, adr_coef
* Write y(n) at DXR
* by saving high part of ACCU in DXR
STH
B, DXR0
* Transfer of the oldest value of 1rst array
* to the oldest value of the 2nd array
MAR
*+AR2(-2)%
MAR
*AR3-%
MVDD
*AR2, *AR3+0%
* Go back to the beginning of the loop
B
debut
ESIEE, Slide 72
See files
firsym.asm
and
fircoef.asm
for the test.
Copyright © 2003 Texas Instruments. All rights reserved.
Tutorial

The listing files for the prceent examples can
be found in directory tutorial:

ESIEE, Slide 73
Tutorial > Dsk5416 > Chapter 14 > Labs_fir
Copyright © 2003 Texas Instruments. All rights reserved.
Implementation of FIR Filters on C55x

Implementation of block filters

Implementation of symmetrical or
asymmetrical FIR filters
ESIEE, Slide 74
Copyright © 2003 Texas Instruments. All rights reserved.
Implementation of FIR Filters using C55x

2 MAC units accessed using 3 data buses
D, B, C make it possible to:


Calculate 2 output samples y at a time using
same set of coefficients and different data x.
Calculate 2 output samples y at a time using
same input data x but 2 set of coefficients.
D a ta R e a d B u s e s
t
M AC
MAC
AC
A0
AC1
ESIEE, Slide 75
Copyright © 2003 Texas Instruments. All rights reserved.
Using the 2 MAC Units

yn
=
Use of block
filtering in order to
calculate 2 output
samples at a time.
b 0 x n + b 1 x n-1 + b 2 x n-2 + b 3 x n-3
D a ta R e a d B u s e s
t
M AC
MAC
AC
A0
AC1
y n+1 = b 0 x n+1 + b 1 x n + b 2 x n-1 + b 3 x n-2
C55x
yn
=
C54x
ESIEE, Slide 76
MAC *AR2+, *CDP+, AC0 :: MAC *AR3+, *CDP+, AC1
b 0 x n + b 1 x n-1 + b 2 x n-2 + b 3 x n-3
MAC *AR2+, *AR3+, A
Copyright © 2003 Texas Instruments. All rights reserved.
Block Filter

Calculate a block of M output samples:


Avoids interrupts sample by sample
Allows calculation of 2 samples at a time
N 1
ynm   bi xn mi
i 0

ESIEE, Slide 77
m   0, M  1.
M+N-1 inputs necessary to calculate M output
samples.
 Because of N-1 initial conditions.
Copyright © 2003 Texas Instruments. All rights reserved.
Block Filter, example N=4, M=3
CDP
Coeffcients
b0
AR2
b1
AR3
b2
b3
Input data
xn
xn-1
xn-2
xn-3
xn-4
xn-5
…
yn = b0xn+b1xn-1+b2xn-2+b3xn-3
yn-1 = b0xn-1+b1xn-2+b2xn-3+b3xn-4
yn-2 = b0xn-2+b1xn-3+b2xn-4+b3xn-5
ESIEE, Slide 78
Copyright © 2003 Texas Instruments. All rights reserved.
Block Filter Example

Double loop:


On coefficients and on m
Coefficients accessed by CDP:

CDP (Cmem) modifications limited to:
*CDP, *CDP+, *CDP-, *(CDP+T0).
 CDP uses
B bus only for dual-MAC.
Because B bus is internal only, coefficients
must also be internal.

ESIEE, Slide 79
Place data operands carefully to avoid
memory conflicts (SA/DARAM).
Copyright © 2003 Texas Instruments. All rights reserved.
Using Dual MAC
y n = b 0 x n + b 1 x n-1 + b 2 x n-2 + b 3 x n-3
y n+1 = b 0 x n+1 + b 1 x n + b 2 x n-1 + b 3 x n-2
CDP
AR2
AR3
B
C
D
CDP
MAC
MAC
AC0
AC1
Coeffcients
b0
AR2
b1
AR3
b2
b3
Input data
xn
xn-1
xn-2
xn-3
xn-4
xn-5
…
MAC *AR2+, *CDP+, AC0 :: MAC *AR3+, *CDP+, AC1
ESIEE, Slide 80
Copyright © 2003 Texas Instruments. All rights reserved.
Initialization of Pointers




Use AMOV to do transfers during the
“AD” pipeline phase.
Init AR2 to point to the 1st value of input
data : (x)
Init AR3 to point to the 2nd value of
input data (x+1)
Init CDP to point to coefficient array (a)
AMOV
AMOV
AMOV
ESIEE, Slide 81
#x,XAR2
#(x+1),XAR3
#a0,XCDP
Copyright © 2003 Texas Instruments. All rights reserved.
Inner Loop on Coefficients
RPT #3
MAC *AR2+,*CDP+,AC0
:: MAC *AR3+,*CDP+,AC1
Pointers at the end of the repeat instruction:
CDP
CDP
ESIEE, Slide 82
Coeffcients
b0
b1
b2
AR2
b3
AR3
AR2
AR3
Input data
xn
xn-1
xn-2
xn-3
xn-4
xn-5
…
Reinitialization of
pointers for next
output sample:
ASUB
ASUB
MOV
#2,AR2
#2,AR3
#a0,CDP
Copyright © 2003 Texas Instruments. All rights reserved.
Circular Addressing Mode for Coefficients




Initialize size of the circular buffer: BK
Set up Buffer Start Address: BSA and
Xeven
Set up ARi or CDP
No memory alignment constraint
b0
BKzz
Xeven : BSAxx
b1
b2
ARn/CDP
b3
ESIEE, Slide 83
Copyright © 2003 Texas Instruments. All rights reserved.
Circular Buffer Addressing Mode
Buffer Start Address =
Offset into Buffer
=
Calculated Address
=
Buffer Length
=
ESIEE, Slide 84
Xeven[22:16]
+
Xeven[22:16]
BSAxx[15:0]
ARn/CDP
BSAxx + ARn/CDP
BKzz[15:0]
Copyright © 2003 Texas Instruments. All rights reserved.
Circular Buffer Addressing Mode
Offset
AR0
AR1
AR2
AR3
AR4
AR5
AR6
AR7
CPD
Xeven
Buffer
Start
Address
XAR0[22:16]
BSA01
Block size
Register
BK03
XAR2[22:16]
BSA01
XAR4[22:16]
BSA01
BK03
XAR6[22:16]
BSA01
XCDP[22:16]
BSAC
BKC
The even XARn (i.e. 0,2,4,6) determines the 64K Page
ESIEE, Slide 85
Copyright © 2003 Texas Instruments. All rights reserved.
Selecting Circular or Linear Addressing
Mode

Use the LSB of Status word ST2_55
15
ST2_55
9 8 7 6 5 4 3 2 1 0
other bits or rsvd
0 = linear mode
C
D
P
L
C
A
R
7
L
C
A
R
6
L
C
A
R
5
L
C
A
R
4
L
C
A
R
3
L
C
A
R
2
L
C
A
R
1
L
C
A
R
0
L
C
1 = circular mode
(default)

Set or reset status bits:
BSET AR5LC
BCLR AR3LC
ESIEE, Slide 86
;AR5 in circular mode
;AR3 in linear mode
Copyright © 2003 Texas Instruments. All rights reserved.
Circular Buffer Exercise
Use AR4 as a circular pointer to x{5}:
A
AR
R44
x
.sect “data”
.int 7,1,9,6,2
.sect “code”
__________________
AMOV #x,XAR4
__________________
MOV #x,BSA45
__________________
MOV #5,BK47
__________________
MOV #0,AR4
__________________
BSET AR4LC
MOV
MOV
MOV
MOV
ESIEE, Slide 87
#3,T0
*(AR4+T0),AC0
*+AR4(#4h),AC1
*AR4(T0),AC2
;init data
;init XAR
;init start addr
;init length
;init AR4 to top
;set AR4 to circ
;index
;AC0 =_7__, AR4 =_3__
;AC1 =_9__, AR4 =_2__
;AC2 =_7__, AR4 =_2__
x
7
1
9
6
2
0
1
2
3
4
Results are
cumulative
Copyright © 2003 Texas Instruments. All rights reserved.
Circular Buffer for Coefficients

Table of coefficients b0 … b3:




Circular buffer addressed by CDP.
Initialize XCDP: 7 MSB
Initialize CDP to 0: offset in the buffer
Set up CPD in circular addressing mode
s1: AMOV
AMOV
AMOV
MOV
MOV
MOV
BSET
ESIEE, Slide 88
#x,XAR2
#a0,XCDP
#(x+1),XAR3
#a0,BSC
#0,CDP
#4,BKC
CDPLC
Copyright © 2003 Texas Instruments. All rights reserved.
Store Results, 32-bit Moves


Assuming fractional mode, 2 results are
in high parts of AC0 and AC1
AC0 and AC1 can be saved separately:
MOV HI(AC0), *AR4+
MOV HI(AC1), *AR4+

AC0, AC1 can be saved at the same time:
MOV pair(hi(AC0)),dbl(*AR4+)



ESIEE, Slide 89
Pairs: (AC0,AC1), (AC2,AC3)
ARi incremented of 2
Even align y
Copyright © 2003 Texas Instruments. All rights reserved.
Block Filter Inner Loop
s1:
e1:
ESIEE, Slide 90
AMOV
AMOV
AMOV
AMO V
MOV
MOV
MOV
BSET
#x,XAR2
#a0,XCDP
#(x+1),XAR3
# y, X A R4
#a0,BSAC
#0,CDP
#4,BKC
CDPLC
MOV
MOV
RPT
MAC
::MAC
ASUB
ASUB
MOV
#0,AC0
#0,AC1
#3
*AR2+,*CDP+,AC0
*AR3+,*CDP+,AC1
#2,AR2
#2,AR3
p ai r ( hi (A C 0) ), d bl ( *A R4 + )
Copyright © 2003 Texas Instruments. All rights reserved.
Outer Loop Using RPTB or RPTBlocal


Use RPTB Repeat Block instruction
We must specifiy:



Start address of the block: next instruction
End address: label specifies last instruction
The number of repetitions counter:



RPTBlocal: executes from the IBU


ESIEE, Slide 91
BRC0: loop counter initialized with count-1
Min count = 2
56 bytes maximum (if > 56 Bytes use RPTB)
Reduces power consumption
Copyright © 2003 Texas Instruments. All rights reserved.
Outer Loop on m: Calculate M yn-m
s1 :
AMO V
#x, XAR2
AMO V
#a0 ,XCD P
AMO V
#(x +1), XA R 3
AMO V
#y, XAR4
MOV
#a0 ,BSA C
MOV
#0, CDP
MOV
#4, BKC
BSE T
CDP LC
MOV
#(( samp s- t aps )/2) ,BR C 0
RPT BLO CA L e1
MOV
#0, AC0
MOV
#0, AC1
RPT
#3
MAC
*AR 2+,* CD P +,A C0
:: MAC
*AR 3+,* CD P +,A C1
ASU B
#2, AR2
ASU B
#2, AR3
e1 :
MOV
pai r(hi (A C 0)) ,dbl (*A R 4+ )
ESIEE, Slide 92
Copyright © 2003 Texas Instruments. All rights reserved.
More Nested loops ?

Nesting RPTB or RPTBlocal:


2 levels supported using BRC0 (outer) and
BRC1/BRS1 (inner)
No saving of registers required for nested
block repeat.
MOV #outer_cnt,BRC0
MOV #inner_cnt,BRC1
RPTBLOCAL outer
. . .
RPTBLOCAL inner
. . .
inner: last_inner
. . .
outer: last outer
ESIEE, Slide 93
;load outer loop count
;load BRC1, auto-load BRS1
;use BRC0
;BRC1: decrements, BRS1-no change
Copyright © 2003 Texas Instruments. All rights reserved.
Laboratory on Block Filter


Implement a block FIR with 16 coefficients
and input block size = 200.
Implement subroutine
C 5 5 10
64 Kx8
ROM
FF_0000h EPtable{16}
1_0000h
code
4000h
FF_FF00h
vectors
6000h
SARAM0 8Kx8
a{16}
DARAM2 8Kx8
x{200}
DARAM3 8Kx8
SP/SSP
5_0000h
AC0
16Kx8
CE0
y
All addresses and lengths are shown in bytes
ESIEE, Slide 94
Copyright © 2003 Texas Instruments. All rights reserved.
Using the Stack and Subroutines



Subroutines require call and ret.
During a call the return address is
stored in the Stack SP.
Let us call fir the subroutine:

ESIEE, Slide 95
call fir
Copyright © 2003 Texas Instruments. All rights reserved.
Initialize the Stack



Declare an unitialized section (.usect) of
appropriate length to reserve space.
Initialize stack pointer to point to the
top of stack +1.
Recommendation: place the stack in
internal memory and align on a 4-byte
boundary:

ALIGN= specifies bytes
0
Size
.set
100h
Stack .usect "STK",size
AMOV
#(stack+size),XSP
Mem
STK
SP
ESIEE, Slide 96
Copyright © 2003 Texas Instruments. All rights reserved.
The System Stack SSP





ESIEE, Slide 97
When a call occurs PC[15:0] is pushed
on the stack
The upper 8 bits SP[23:16] are pushed
on the system stack accessed by SSP
System Stack Pointer.
CFCT is used to store the active loop
context.
WSP and XSSP share the same upper 7
bits.
Place SP and SSP with care to avoid
dual-access delays.
Copyright © 2003 Texas Instruments. All rights reserved.
Data Types



Byte: 8 bits
Word: 16 bits
Long: 32 bits

Long access assumes address points to MSW




LSW read from same address with LSB toggled.
Ptr=100h, MSW=100h, LSW = 101h
Ptr=101h, MSW=101h, LSW = 100h
To ensure proper alignment:


Constants (int, long) are automatically aligned on
type boundaries
Variables:


16 bit: no problem
32 bits use: use the even-align flag:

ESIEE, Slide 98
.usect “vars”,Nwords,,1
Copyright © 2003 Texas Instruments. All rights reserved.
Solution: Declarations
x0
stklen
a0
y0
BOS
BOSS
.sect "indata"
.copy in7.dat
.def start
.cpl_off
.arms_off
.c54cm_off
.set 100
.usect "coeffs",16,1,1
.usect "results",200,1,1
.usect "STK", stklen,1,1
.usect "SSTK",stklen,1,1
.sect "init"
table
ESIEE, Slide 99
.int
.int
.int
.int
7FCh,
800h,
803h,
7FFh,
7FDh,
801h,
802h,
7FEh,
7FEh,
802h,
801h,
7FDh,
7FFh
803h
800h
7FCh
Copyright © 2003 Texas Instruments. All rights reserved.
Solution: Code
sect "code"
.DP a0
.
start:
here:
ESIEE, Slide 100
AMOV #BOS+stklen,XSPc ;set up Stack +
MOV #BOSS+stklen,SSP ;System Stack Ptrs
CALL copy
;copy coeffs
BSET FRCT
BSET M40
BSET SXMD
;turn on mult. shift
;turn on 40 bit math
;turn on sign exten.
CALL fir
nop
B
here
;perform fir
;stop
Copyright © 2003 Texas Instruments. All rights reserved.
Solution: Subroutine copy
copy:
AMOV #table,XAR2
;load pointers
AMOV #a0,XAR3
RPT #7
MOV dbl(*AR2+),dbl(*AR3+)
;move from table to a
RET
ESIEE, Slide 101
Copyright © 2003 Texas Instruments. All rights reserved.
Solution: Subroutine fir
fir: MOV #92,BRC0
;block repeat count
AMOV #x0,XAR2
;initialize pointers
AMOV #x0+1,XAR3 ;for data,
AMOV #y0,XAR4
;results
AMOV #a0,XCDP
;and coeffiecients
MOV #a0,BSAC
;buffer start address
MOV #16,BKC
;buffer size
MOV #0, CDP
;index
BSET CDPLC ;turn on circ adr CDP
end
ESIEE, Slide 102
RPTBlocal end
MPYM *AR2+,*CDP ,AC0 ;AC0 1st product
MPYM *AR3+,*CDP+,AC1 ;AC1 gets 2nd prd
RPT #14
MAC *AR2+,*CDP+,AC0
;form results
:: MAC *AR3+,*CDP+,AC1
MOV pair(hi(AC0)),dbl(*AR4+)
;store AC0/AC1
ASUB #14,AR2
;wrap data pointers
ASUB #14,AR3
;next calculation
RET
Copyright © 2003 Texas Instruments. All rights reserved.
Implementation of Symmetrical and
Anti-symmetrical FIR filters on ‘C55x
Symmetrical
Anti-symmetrical
Coeff
s
Coeff
s
b0 b1 b2 b3
b0 b1 b2 b3 b4 b5 b6 b7


b4 b5 b6 b7
These filters may be “folded” and performed with N adds and N/2 MACs
Filters need to be designed as even length
N
1
2
y (n)   b(i )  x(n  i )  x(n  N  1  i )  N even.
i 0
ESIEE, Slide 103
Copyright © 2003 Texas Instruments. All rights reserved.
Instructions FIRSADD and FIRSSUB

FIRSADD Xmem,Ymem, coef,Acx,Acy




FIRSSUB Xmem,Ymem, coef,Acx,Acy





ESIEE, Slide 104
Acy = Acy + (Acx x (*CDP))
|| Acx = Xmem + Ymem
For symmetrical FIR
Acy = Acy + (Acx x (*CDP))
|| Acx = Xmem - Ymem
For anti-symmetrical FIR
If performing a block FIR, dual MAC has
better performance than FIRS.
A design consideration for migration from
‘C54x.
Copyright © 2003 Texas Instruments. All rights reserved.
Comparison of C54x and C55x

2 MAC in ‘C55x versus 1 for C54x


Circular addressing modes:



ESIEE, Slide 105
Well suited for block filtering and 2 taps
per cycle time instead of 1 (for large N).
3 BK registers in C55X instead of 1 in
‘C54x: allows for several simultaneous
circular buffers with different size.
In C54x, circular addressing mode is
specified in indirect addressing type % in
the instructions.
In C55x, the mode in set in status register
ST2_55 for each register (linear or
circular). No memory alignment constraint.
Copyright © 2003 Texas Instruments. All rights reserved.
Comparison of C54x and C55x
Symmetrical and Anti-symmetrical
FIR Filters

In C54x, instruction FIRS:


In C55x, instructions FIRSADD +
FIRSSUB:


ESIEE, Slide 106
Allows 2 taps/cycle for a symmetrical FIR
Allow us to efficiently implement
symmetrical and anti-symmetrical FIRs.
Despite the 2 MACs, as there is only 1 ALU,
again 2 taps/cycle for symmetrical or antisymmetrical FIRs.
Copyright © 2003 Texas Instruments. All rights reserved.
Follow On Activities on 5416 DSK

Laboratory 3 for TMS320C5416 DSK


Laboratory 4 for TMS320C5416 DSK


To determine by experiment how many FIR
coefficients are required for acceptable audio
quality.
Application 4 for TMS320C5416 DSK

ESIEE, Slide 107
To determine by practical experiment the best FIR
window functions for audio.
Electronic Crossover for multiple loudspeaker
system. Divides audio signal into treble and bass at
16 different selectable frequencies using FIR
filters.
Copyright © 2003 Texas Instruments. All rights reserved.
Follow on activities on 5510 DSK

Application “delays and echo” for
TMS320C5510 DSK

ESIEE, Slide 108
Simulates delays in communications
networks and reflection of sound heard in a
canyon. Introduces circular buffers and the
configuration used for a Finite Impulse
Response (FIR) filter.
Copyright © 2003 Texas Instruments. All rights reserved.