1. DSP C5000 Chapter 14 Finite Impulse Response (FIR) Filter Implementation Copyright © 2003 Texas Instruments. All rights reserved.

2. ESIEE, Slide 2Outline Digital Filters and FIR filters Digital Filters and FIR filters Implementation of FIR Filters on C54x Implementation of FIR Filters on C54x Implementation of FIR Filters on C55x Implementation of FIR Filters on C55x Comparison of C54x and C55x Comparison of C54x and C55x

3. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 3 Outline of FIR Filters  Generalities on Digital Filters Generalities on Digital Filters Generalities on Digital Filters  FIR Filters with Matlab FIR Filters with Matlab FIR Filters with Matlab  Implementation of FIR Filters Implementation of FIR Filters Implementation of FIR Filters

4. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 4 Digital Filters

5. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 5 Linear, Time-Invariant Digital Systems  Linearity  Time Invariance

6. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 6 Impulse Response

7. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 7 Input-Output Relationship, Convolution

8. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 8 Input-Output Relationship, Convolution  Using linearity and time invariance:

9. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 9 Output for a Single Frequency Input  Single frequency input  Single frequency output

10. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 10 Frequency Transfer Function  For a digital filter the frequency transfer function is periodic. Phase Group delay Amplitude

11. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 11 Relationship Between Fourier Transforms of Input and Output

12. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 12 Z Transfer Function

13. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 13 Basic Relationships of a Digital Filter

14. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 14 Rational z Transfer Function  Linear equation with constant coefficients.

15. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 15 IIR and FIR Filters  IIR = Infinite Impulse Response  FIR = Finite Impulse Response  FIR  IIR

16. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 16 FIR and IIR  FIR: output y n is a linear combination of a finite number of input samples.  IIR: output y n is a linear combination of a finite number of input and of output samples. Recursive form.

17. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 17 Causality and Stability  A filter is causal if h n =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:

18. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 18 Representation of Poles and Zeroes of H(z) in the Complex Plane

19. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 19 Some Useful Matlab Functions  Example for a FIR filter:  Enter the filter coefficients vector b:  b=[1 1 1 1]; a=1;  Calculate transfer function Hf, its amplitude and phase on 256 samples, with fs=1:  [Hf,f]=freqz(b,a,256,1);  HfA=abs(Hf);  Hfphi=angle(Hf);

20. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 20 Some Useful Matlab Functions  Plot impulse response: stem(b)  Plot amplitude and phase of transfer function: plot(f,HfA) and plot(f,Hfphi)

21. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 21 Some Useful Matlab Functions  Generate a test signal = sum of cosines:  x=cos(2*pi*[0:99]*0.25)+2*cos(2*pi*[0:99]*0.1);  Apply the filter to x. Output is y:  y=filter(b,a,x);  Plot the results: plot(x); plot(y) x is the sum of 2 frequencies : 0.25 and 0.1. The filter cancels the frequency 0.25. y has only the freq. 0.1.

22. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 22 Calculation of a FIR using Matlab  For given attenuation and frequency response characteristics, the transfer function can be calculated using different methods:  Mean square error, miniMax (Chebychev)  Empirical window method  Corresponding Matlab functions  firls and remez.  fir and fir1.

23. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 23 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.

24. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 24 Example using Matlab  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);

25. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 25 Results of Matlab Example  The minimum orders to satisfy the constraints are 23 for LS, 21 for minimax and 25 for the window method. Mini Max window Least square method Window method

26. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 26 Results of Matlab Example  Impulse Response hn n

27. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 27 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).  The phase will be linear or affine.  2 possible cases:  symmetrical or asymmetrical FIR.  Constant group delay = T S (N-1)/2  Symmetrical: h(n)=h(N-1-n)  Asymmetrical; h(n)=-h(N-1-n)

28. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 28 FIR filters with Constant Group Delay or Linear Phase  Asymmetric case: linear phase  Asymmetrical case:

29. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 29 Fixed Point Implementation of FIR Filters Numerical Issues  Fixed point implementation:  16 bits for data and coefficients  Accumulators have size 40 bits  Fixed point representation of data  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:  Bi = log 2 (hmax)  Coefficients in Qk’ with k = 16-Bi

30. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 30 Matlab Example  The coefficients Bre can be quantized using 16-bit fixed point with 15 fractional bits:  Bre=round(Bre*2^15);  To store the result in a text file for CCS:  fp=fopen('coef.asm','wt')  for i=1:22  fprintf(fp,'.word %d \n',Ba(i))  end  fclose(fp)

31. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 31 Matlab Example  File coef.asm  Can be edited to be used with CCS.

32. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 32 FIR Implementation, Numerical issues, FRCT bit  Common case:  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.

33. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 33 Structures for FIR Implementation  Common structures for FIR filters  Transversal structures  Trellis structure  Useful in some adaptive situations.  Transversal structures using:  Linear buffers  Circular buffers  Special case for symmetrical or asymmetrical FIRs.

34. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 34 Transversal Structures of FIR  Structure with a delay line  Transposed structure

35. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 35 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 T S  ACCU=0  for i=0 to N-1:  Multiply h(i) by x(n-i) and add it to accumulator  Output y(n)

36. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 36 Implementation of FIR Filters on C54x  Implementation of General Transversal FIR filters Implementation of General Transversal FIR filters Implementation of General Transversal FIR filters  Using linear buffers  Using circular buffers  Implementation of Symmetrical FIR filters Implementation of Symmetrical FIR filters Implementation of Symmetrical FIR filters

37. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 37 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  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.

38. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 38 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  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)

39. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 39 MACD Instruction  MACD:  Multiply Accumulate and Delay move.  MACD Smem, pmad, src  src=src+Smem*pmad;  T=Smem;  (Smem+1)=Smem  If MACD used in a loop with RPT the program memory (pmad) address is automatically incremented.  MACD alone = 3 cycle times  In a RPT loop 1 cycle time

40. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 40 Implementing a FIR with MACD  Memory organization of data and coefficients

41. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 41 Initialization of Registers  STM Stores #value to the MMR early in the pipeline to avoid latencies.  2 words, 2cycles.  Initialization of FRCT bit (fractional mode):  Instructions SSBX (Set Status Bit) and RSBX (Reset Status Bit).  Initialization of ACCU  Using RPTZ :RePeaT after initializing ACCU at 0  Or via LD #0,A

42. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 42 RPT, RPTZ Instructions  RPT #n  Repeat next instruction n+1 times. Repetition counter set to n and decreases until 0.  1 or 2 cycles, not interruptible.  RPTZ src, #n  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).

43. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 43 Implementing a FIR Filter with MACD  Test with CCS  Filter with N=32 coefficients all equal to 1/32  Create a file fircoef.asm, address of coefficients in program mem = adr_coef

44. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 44 Implementing a FIR Filter with MACD  File containing coefficients fircoef.asm

45. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 45 Implementing a FIR Filter with MACD  File firmacd.asm with the program  2 files to compile and link:  fircoef.asm and firmacd.asm  Test by associating files on the ports DRR0 and DXR0  File infir.dat attached to DRR0  File outfir.dat attached to DXR0

46. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 46 Implementing a FIR Filter with MACD  Program file firmacd.asm: initializations

47. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 47 Implementing a FIR Filter with MACD  Program file firmacd.asm: endless loop See files firmacd.asm and fircoef.asm for the test in directory tutorial.

48. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 48 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:  A value 0.5 (0x4000) then zeros (at least 40)  Set 2 probe points  1 at reading of DRR: LDM DRR  1 at end of loop: B debut  Attach files to probe points  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)

49. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 49Results  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).  Plot a time graph (Single Time)  Plot a frequency graph (FFT: Magnitude and Phase)

50. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 50 Results for the impulse response and its FFT

51. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 51 Second Test  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.

52. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 52 Second test  Observe that the output is attenuated and is phase shifted by values corresponding at H(f) at f S /40.

53. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 53 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.  The 2 extreme words of the memory block are considered as contiguous.  Characteristics of a circular buffer:  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.

54. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 54 Trace of Memory and Pointer in a Circular Buffer of Length 3

55. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 55 FIR with Circular Buffers  2 circular buffers  1 for data  1 for coefficients

56. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 56 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  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

57. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 57 Instruction MAC with 2 operands in Indirect Addressing Mode  MAC: Multiply and Accumulate  MAC Xmem, Ymem, src[, dest]  dst=src+Xmem*Ymem  T=Xmem  With Xmem, Ymem use only AR2 to AR5  Can be executed in 1 cycle time.  Dual operand instructions indirect addressing restricted to:  AR2, AR3, AR4, AR5  none, +, -, +0%

58. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 58 Circular Buffer with C54x  Circular indirect addressing mode:  *ARi-%, *ARi+%, *ARi-0%, *ARi+0%, *ARi(lk)%  In dual operand mode Xmem, Ymem:  *ARi+0% only valid mode  To perform a decrement, store a negative value in AR0.  BK register:  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.

59. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 59 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:  for N=32, 6 LSB of start address =0  for N=30, 5 LSB of start address =0  To access a circular buffer:  Initialize BK with N (nb bits)  Choose 1 ARi as a pointer  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.

60. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 60 Circular buffer on C54x

61. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 61 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  Start addresses must be multiple of 64.  First step of program after initialization:  Transfer coefficients from program to data memory from adr_coef to adr_debut_coef.

62. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 62 Move Instructions  MVPD #pmad, Smem  Copy values from program to data memory  In RPT mode pmad is automatically incremented.

63. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 63 Implementation of FIR with 2 Circular Buffers, Initializations

64. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 64 Implementation of FIR with 2 Circular Buffers, Program See files fircirc.asm and fircoef.asm for the test.

65. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 65 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:  buf_data align(64) > DATApage 1

66. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 66 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.

67. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 67 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  B = B + A(32:16) x Pmem addressed by PAR  A = (Xmem+Ymem)<<16  PAR=PAR+1  RC=RC-1

68. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 68 Using FIRS for a Symmetrical FIR Filter  3 arrays:  N/2 first coefficients,  N/2 newest data and N/2 oldest data.

69. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 69 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)

70. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 70 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):  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).

71. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 71 Symmetrical FIR Implementation with FIRS, Initializations

72. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 72 Symmetrical FIR Implementation using FIRS, Program See files firsym.asm and fircoef.asm for the test.

73. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 73Tutorial  The listing files for the prceent examples can be found in directory tutorial:  Tutorial > Dsk5416 > Chapter 14 > Labs_fir

74. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 74 Implementation of FIR Filters on C55x  Implementation of block filters Implementation of block filters Implementation of block filters  Implementation of symmetrical or asymmetrical FIR filters Implementation of symmetrical or asymmetrical FIR filters Implementation of symmetrical or asymmetrical FIR filters

75. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 75 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.

76. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 76 Using the 2 MAC Units  Use of block filtering in order to calculate 2 output samples at a time.

77. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 77 Block Filter  Calculate a block of M output samples:  Avoids interrupts sample by sample  Allows calculation of 2 samples at a time  M+N-1 inputs necessary to calculate M output samples.  Because of N-1 initial conditions.

78. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 78 Block Filter, example N=4, M=3

79. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 79 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.  Place data operands carefully to avoid memory conflicts (SA/DARAM).

80. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 80 Using Dual MAC

81. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 81 Initialization of Pointers  Use AMOV to do transfers during the “AD” pipeline phase.  Init AR2 to point to the 1 st value of input data : (x)  Init AR3 to point to the 2 nd value of input data (x+1)  Init CDP to point to coefficient array (a)

82. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 82 Inner Loop on Coefficients Pointers at the end of the repeat instruction: Reinitialization of pointers for next output sample:

83. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 83 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

84. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 84 Circular Buffer Addressing Mode

85. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 85 Circular Buffer Addressing Mode The even XARn (i.e. 0,2,4,6) determines the 64K Page

86. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 86 Selecting Circular or Linear Addressing Mode  Use the LSB of Status word ST2_55  Set or reset status bits:

87. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 87 Circular Buffer Exercise Use AR4 as a circular pointer to x{5}: Results are cumulative

88. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 88 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

89. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 89 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:  AC0, AC1 can be saved at the same time:  Pairs: (AC0,AC1), (AC2,AC3)  ARi incremented of 2  Even align y

90. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 90 Block Filter Inner Loop

91. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 91 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:  BRC0: loop counter initialized with count-1  Min count = 2  RPTBlocal: executes from the IBU  56 bytes maximum (if > 56 Bytes use RPTB)  Reduces power consumption

92. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 92 Outer Loop on m: Calculate M yn-m

93. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 93 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.

94. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 94 Laboratory on Block Filter  Implement a block FIR with 16 coefficients and input block size = 200.  Implement subroutine

95. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 95 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:  call fir

96. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 96 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

97. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 97 The System Stack SSP  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.

98. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 98 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: .usect “vars”,Nwords,,1

99. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 99 Solution: Declarations.sect "indata" x0.copy in7.dat.def start.def start.cpl_off.arms_off.c54cm_off stklen.set100 a0.usect "coeffs",16,1,1 y0.usect "results",200,1,1 BOS.usect "STK", stklen,1,1 BOSS.usect "SSTK",stklen,1,1.sect "init".sect "init" table.int 7FCh, 7FDh, 7FEh, 7FFh.int 800h, 801h, 802h, 803h.int 800h, 801h, 802h, 803h.int 803h, 802h, 801h, 800h.int 803h, 802h, 801h, 800h.int 7FFh, 7FEh, 7FDh, 7FCh

100. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 100 Solution: Code. sect "code".DP a0 start:AMOV #BOS+stklen,XSPc ;set up Stack + MOV #BOSS+stklen,SSP ;System Stack Ptrs CALL copy ;copy coeffs BSET FRCT ;turn on mult. shift BSET M40 ;turn on 40 bit math BSET SXMD ;turn on sign exten. CALL fir;perform fir nop nop here:B here ;stop

101. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 101 Solution: Subroutine copy copy: AMOV #table,XAR2;load pointers AMOV #a0,XAR3 RPT #7 MOV dbl(*AR2+),dbl(*AR3+) MOV dbl(*AR2+),dbl(*AR3+) ;move from table to a RET

102. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 102 Solution: Subroutine fir fir: MOV #92,BRC0;block repeat count AMOV #x0,XAR2 ;initialize pointers AMOV #x0,XAR2 ;initialize pointers AMOV #x0+1,XAR3 ;for data, AMOV #x0+1,XAR3 ;for data, AMOV #y0,XAR4;results AMOV #y0,XAR4;results AMOV #a0,XCDP;and coeffiecients AMOV #a0,XCDP;and coeffiecients MOV #a0,BSAC;buffer start address MOV #a0,BSAC;buffer start address MOV #16,BKC;buffer size MOV #16,BKC;buffer size MOV #0, CDP;index MOV #0, CDP;index BSET CDPLC;turn on circ adr CDP BSET CDPLC;turn on circ adr CDP RPTBlocal end MPYM *AR2+,*CDP,AC0 ;AC0 1st product MPYM *AR2+,*CDP,AC0 ;AC0 1st product MPYM *AR3+,*CDP+,AC1 ;AC1 gets 2 nd prd MPYM *AR3+,*CDP+,AC1 ;AC1 gets 2 nd prd RPT #14 RPT #14 MAC *AR2+,*CDP+,AC0 ;form results MAC *AR2+,*CDP+,AC0 ;form results :: MAC *AR3+,*CDP+,AC1 :: MAC *AR3+,*CDP+,AC1 MOV pair(hi(AC0)),dbl(*AR4+);store AC0/AC1 MOV pair(hi(AC0)),dbl(*AR4+);store AC0/AC1 ASUB #14,AR2 ;wrap data pointers ASUB #14,AR2 ;wrap data pointers end ASUB #14,AR3;next calculation RET RET

103. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 103 Implementation of Symmetrical and Anti-symmetrical FIR filters on ‘C55x   These filters may be “folded” and performed with N adds and N/2 MACs   Filters need to be designed as even length

104. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 104 Instructions FIRSADD and FIRSSUB  FIRSADD Xmem,Ymem, coef,Acx,Acy  Acy = Acy + (Acx x (*CDP))  || Acx = Xmem + Ymem  For symmetrical FIR  FIRSSUB Xmem,Ymem, coef,Acx,Acy  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.

105. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 105 Comparison of C54x and C55x  2 MAC in ‘C55x versus 1 for C54x  Well suited for block filtering and 2 taps per cycle time instead of 1 (for large N).  Circular addressing modes:  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.

106. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 106 Comparison of C54x and C55x Symmetrical and Anti-symmetrical FIR Filters  In C54x, instruction FIRS:  Allows 2 taps/cycle for a symmetrical FIR  In C55x, instructions FIRSADD + FIRSSUB:  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 anti- symmetrical FIRs.

107. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 107 Follow On Activities on 5416 DSK  Laboratory 3 for TMS320C5416 DSK  To determine by practical experiment the best FIR window functions for audio.  Laboratory 4 for TMS320C5416 DSK  To determine by experiment how many FIR coefficients are required for acceptable audio quality.  Application 4 for TMS320C5416 DSK  Electronic Crossover for multiple loudspeaker system. Divides audio signal into treble and bass at 16 different selectable frequencies using FIR filters.

108. Copyright © 2003 Texas Instruments. All rights reserved. ESIEE, Slide 108 Follow on activities on 5510 DSK  Application “delays and echo” for TMS320C5510 DSK  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.