1. ENCM515 Standard and Custom FIR filters*
07/16/96
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ENCM515 Standard and Custom FIR filters
M. R. Smith, Electrical and Computer Engineering
University of Calgary, Canada
ucalgary.ca *

2. ENCM515 -- High speed FIR filters Copyright smithmr@ucalgary.ca
Compare performance of
optimized “C” code -- coded the “best way” (software circular buffer using “if” statements or using pointer “mask operations” -- your choice”
hand coded non-parallel code
hand coded parallel code for FIR filter operations
Compare your optimized code with what is available in DSP library files in VisualDSP directories
Need to show filter works -- OFFLINE
Test audio performance
Write a suitable report discussing results.
10/7/2019
ENCM High speed FIR filters Copyright

3. ENCM515 -- High speed FIR filters Copyright smithmr@ucalgary.ca
Delay is not only thing to take into account Four paths from 2 sources in front
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4. Transfer function h30(f)
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5. ENCM515 -- High speed FIR filters Copyright smithmr@ucalgary.ca
FIR schematic diagram
Find the Hcoeffs from Bessinger thesis -- convert to floats
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ENCM High speed FIR filters Copyright

6. ENCM515 -- High speed FIR filters Copyright smithmr@ucalgary.ca
Result we need to get
LEFT_EAR = LEFT_SOUND * FIR H_ RIGHT_SOUND * FIR H330
RIGHT_EAR = LEFT_SOUND * FIR H_ RIGHT_SOUND * FIR H30
Take it a step at a time
Get 1 H30 FIR filter to work -- Cut and paste to get timing for 4 FIR -- cache implications here
Test using MONO | IMPULSE
Output identical to FIR coefficients
Audio-wise -- Try H_30 on both ears next
Finally use H_ never been satisfied with gain
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ENCM High speed FIR filters Copyright

7. Coding Characteristics
4 FIR filters associated with 2 sound sources
Bessinger Thesis describes 32 coefficients for each filter
Actually only 2 sets of filter coefficients need to be stored because of system symmetry.
Warning -- convert delay lines to store “float values”
Warning -- convert coefficients to float values not integer.
Need to store current and 31 previous sound values as a minimum.
Will need both left and right delay lines
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ENCM High speed FIR filters Copyright

8. General Concept for Real Time FIR code
For ever {
ReadSource(&left_ear, &right_ear);
arrayleft[N-1] = leftear
arrayright[N-1] = rightear
leftear = rightear = 0;
// Two FIR filter h(0, 30) -- will need 2 more
for (count = 0, count < FIRlength - 1, count++) {
leftear = leftear + arrayleft[count] * fir(count); // convert to pointer ops!!
rightear = rightear + arrayright[count]* fir[count]; }
// Handle delay component of FIR via Memory Move
for (count = 1, count < FIRlength - 1, count++) {
arrayleft(count - 1) = arrayleft(count);
arrayright(count - 1) = arrayright(count); }
WriteSource(leftear, rightear); //
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ENCM High speed FIR filters Copyright

9. FIR code -- impliment in “C”
DM float arrayleft[N], arrayright[N], PM float FIR[N]
void ProcessSound( int leftear, int rightear, int *newleft, int *newright) { float left, right;
arrayleft[N-1] = (float) leftear WHY FLOAT?
arrayright(N-1) = (float) rightear
left = right = 0;
// Two FIR filter h(0, 30) -- need 2 more
for (count = 0, count < FIRlength - 1, count++) {
left = left + arrayleft[count] * fir(count); // Use pointer ops
right = right + arrayright[count]* fir[count]; }
// Handle delay component of FIR
for (count = 1, count < FIRlength - 1, count++) {
arrayleft(count - 1) = arrayleft(count);
arrayright(count - 1) = arrayright(count); }
*newleft = (int) left;
*newright = (int) right; //
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ENCM High speed FIR filters Copyright

10. Practical findings -- FIR
My FIR filters directly in assembly code but no optimizing (meaning no pipelining, no folding of coefficients to take into account symmetry, nothing fancy at all).
Obvious distortions in audio signal (missing samples) when implemented 4 FIRs (hardware loops each with 4 cycles).
Suggestions -- get 1 FIR filter to work using “OFFLINE” and “IMPULSE”. Why?
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ENCM High speed FIR filters Copyright

11. FIR filter -- practical concepts
When testing the filter operations DON'T USE the true filter to start with. Instead test the filter responses as follows
float h30[32] = { }; float h330[32] = { };
Then test (OFFLINE) with h30[ ] loop, then h330[ ] loop, then both. This should give a signal with zero delay???????
When using real h30 or h might be useful to have some method to control overall filter gain -- see next slide for my approach
When implementing filters watch out for “1-outness” in memory position/accesses
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ENCM High speed FIR filters Copyright

12. Testing -- FIR filter gain and deafness
Filter gain is not unity -- not sure you want it unity. Add the following code to main() to control gain in real time without recompiling (or else you’ll go deaf -- what you say?)
float h30gain = 1.0; ditto for h330[]
float h[30] = { etc. }
main( ) {
for (count = 0; count < 32, count++) h30[count] = h30[count] * h30gain;
Change value of h30gain with debugger before running the code.
Make sure you re-download the code before running again -- Why?
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13. Special Properties -- FIR filters in “C”
float array[ARRAYLENGTH]
oldest input stored first -- position 0
newest input stored last -- position ARRAYLENGTH - 1
THIS MEANS float fircoeff[FIRLENGTH]
coefficient a0 stored last -- position FIRLENGTH - 1
pm float *firpt = &fircoeff[FIRLENGTH - 1];
float *arraypt = &array[ARRAYLENGTH - 1];
float result = 0;
for (count = 0; count < FIRLENGTH; count++) {
result = result + (*firpt) * (*arraypt);
firpt--;
arraypt--; }
result = result / gain;
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ENCM High speed FIR filters Copyright

14. Look ahead to future concerns*
07/16/96
When we use use “hardware circular” buffers then the line
float *arraypt = &array[ARRAYLENGTH - 1];
SHOULD not be present as arraypt will be stored in some sort of non-volatile global index register and accessing a circular buffer
This means that we ensure that arraypt is returned to its previous value after using it.
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ENCM High speed FIR filters Copyright *

15. Generic FIR filters in “C”
float *arraypt = &array[ARRAYLENGTH - 1]; -- Done ONCE during setup
Inside the FIR routine -- FIR COEFFICIENTS ARE NOT IN A CIRC BUFFER
float *firpt = &fircoeff[FIRLENGTH - 1]; MAY NOT STAY TRUE
float result = 0; SEE NEXT SLIDE
for (count = 0; count < FIRLENGTH; count++) {
result = result + (*firpt) * (*arraypt);
firpt--;
arraypt--; }
// Need to restore arraypt to original position
arraypt = arraypt + FIRLENGTH (or is it FIRLENGTH + 1)
// Can be handled by Modify(arraypt, FIRLENGTH)
// and many other approaches
result = result / gain;
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16. Multiple FIR filters -- very easy
PM float *firpt = &fircoeff_H30[FIRLENGTH - 1];
float result = 0;
for (count = 0; count < FIRLENGTH; count++) {
result = result + (*firpt) * (*arraypt);
firpt--;
arraypt--; }
result30 = result
arraypt = arraypt + FIRLENGTH -- reset to start of array
firpt = &fircoeff_H330[FIRLENGTH - 1];
for (count = 0; count < FIRLENGTH; count++) { /* Identical code */
finalresult = result + result // Repeat for other ear
arraypt = arraypt + FIRLENGTH etc
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ENCM High speed FIR filters Copyright

17. Speed -- L and R Generic FIR filters
float result, result2 = 0;
for (count = 0; count < FIRLENGTH; count++) {
value = *firpt;
result = result + value * (*arraypt_left);
result2 = result2 + value * (*arraypt_right);
firpt--;
arraypt_left--; arraypt_right--; }
Speed improvement -- less access of FIR coefficients
CAN ALSO get more speed with folding FIR coefficients if symmetric -- h30 but not h330
for (count = 0; count < FIRLENGTH / 2; count++) {
value = *firpt;
result = result + value * ( (*arraypt) *(arraypt - LENGTH + count)) ;
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18. FIR filters in assembly code -- not circular buffer
.extern array
.extern fircoeff <-- put into pm memory?
#define firpt IPM_register?
#define arraypt IDM_register?
#define result float_register?
#define temp1, temp2, temp float_register?????
// float *firpt = &fircoeff[FIRLENGTH - 1];
firpt = fircoeff + FIRLENGTH - 1; <- NOT AN ADDITION -- CONSTANTS ONLY
// float *arraypt = &array[ARRAYLENGTH - 1];
arraypt = array + ARRAYLENGTH - 1; <- NOT AN ADDITION
result = 0.0; // float result = 0;
for (count = 0; count < FIRLENGTH; count++) { // *firpt, *arraypt, firpt--, arraypt--;
temp1 = dm(firpt, -1), temp2 = pm(arraypt, -1)
temp3 = temp1 * temp2; // (*firpt) * (*arraypt)
result = result + temp3 }
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ENCM High speed FIR filters Copyright

19. FIR filters -- Software circular buffer -- Pseudocode
// float *firpt = &fircoeff[FIRLENGTH - 1];
firpt = fircoeff + FIRLENGTH - 1; // float *arraypt = &array[ARRAYLENGTH - 1];
NOTE: array <= arraypt <= array + ARRAYLENGTH - 1;
result = 0.0; // float result = 0;
for (count = 0; count < FIRLENGTH; count++) { // *firpt, *arraypt, firpt--, arraypt--;
temp1 = dm(firpt, -1), temp2 = pm(arraypt, -1)
temp3 = temp1 * temp2; // (*firpt) * (*arraypt)
result = result + temp3;
R1 = arraypt // Handle circular buffer operations
R2 = array
compare (R1, R2) // Can’t compare I registers?
if GE jump(PC, OKAY); // NOT delayed branch
R2 = array + ARRAYLENGTH arraypt = R2
OKAY:
} // endfor // Remember to adjust back arraypt before exitting
10/7/2019
ENCM High speed FIR filters Copyright

20. ENCM515 -- High speed FIR filters Copyright smithmr@ucalgary.ca
10/7/2019
ENCM High speed FIR filters Copyright

21. ENCM515 -- High speed FIR filters Copyright smithmr@ucalgary.ca
Register allocations
Interrupt routines already using Alternate B0, I0, L0, B1, I1, L1
Suggest you control left storage and right storage of sounds using B2 for left and B3 for right -- hence the question from Lab. 2 about using only 1 pointer
Query -- do we ALSO need to add the sound delays from Lab.2 on top of the FIR delay?
Read thesis and check.
WATCH OUT -- my code uses I8,L8,B8
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ENCM High speed FIR filters Copyright

22. FIR filters -- Some rough assembly language concepts
// float *firpt = &fircoeff[FIRLENGTH - 1];
firpt = fircoeff + FIRLENGTH - 1; <- NOT AN ADDITION -- use MODIFY // float *arraypt = &array[ARRAYLENGTH - 1];
NOTE: array <= arraypt <= array + ARRAYLENGTH - 1;
result = 0.0; // float result = 0;
#define saveOldI3 R???
saveOldI3 = arraypt // <-- KEY OPERATION
for (count = 0; count < FIRLENGTH; count++) { // *firpt, *arraypt, combined with firpt--, arraypt--;
temp1 = dm(firpt, -1), temp2 = pm(arraypt, -1) // <-- POST-MOD
temp3 = temp1 * temp2; // (*firpt) * (*arraypt)
result = result + temp3;
// Circular buffer operations automatic }
arraypt = saveOldI // <-- KEY OPERATION
// ?? Where is new sound value added --
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23. Important things to note
Circular buffers only work on Post-modify instructions
can’t use R2 = dm(count, I2)
If interrupt routines are too slow then will lose output signals
21k interrupts currently block each other automatically
Timer interrupt is low priority compared to Serial Port interrupt -- See table Page 3-25
Both interrupts are using the circular buffers -- Race condition occurring
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ENCM High speed FIR filters Copyright

24. Current Loop -- 3 * FIRLENGTH cycles
EH?? -1 and DM/PM access
Above is PSEUDOCODE
Allowed but slow or not allowed?
NOTE: -- Will give correct theoretical timing, but what things are wrong with the code?
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25. Also see CCI articles by Smith
Example to use for Systematic Approach to optimizing DSP algorithm for FIR filter
Also see CCI articles by Smith

26. ENCM515 -- High speed FIR filters Copyright smithmr@ucalgary.ca
Step 1 -- unroll loop
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27. Step 2 -- Identify independence
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28. Step 3 -- refill ALU/Memory pipeline
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29. ENCM515 -- High speed FIR filters Copyright smithmr@ucalgary.ca
Step 4 -- refold loop
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30. ENCM515 -- High speed FIR filters Copyright smithmr@ucalgary.ca
Comparison of loops
Time * FIRLENGTH
Time 5 + FIRLENGTH - 2
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31. ENCM515 -- High speed FIR filters Copyright smithmr@ucalgary.ca
Key issue or not
Current loop shows both dm[ ] and pm[ ] access occurring with a constant post-modify value (-1)
I claim that this is legal but causes a processor stall so that takes extra cycles
No need to use preset modify registers minus1dm and minus1pm unless really worried about speed -- True or False?
10/7/2019
ENCM High speed FIR filters Copyright

32. ENCM515 -- High speed FIR filters Copyright smithmr@ucalgary.ca
Lab. 4
Compare performance of
optimized “C” code -- coded the “best way” (software circular buffer using “if” statements or using pointer “mask operations” -- your choice”
hand coded non-parallel code
hand coded parallel code for FIR filter operations
Compare to what is used in library files
Need to show filter works -- OFFLINE
Test audio performance
Write a suitable report discussing results.
10/7/2019
ENCM High speed FIR filters Copyright