1. DSP 'Swiss Army Knife' Team M3: Jacob Thomas Nick Marwaha Darren Shultz Craig T. LeVan Project Manager: Zachary Menegakis Overall Project Objective: General purpose Digital Signal Processing chip Stage 2 | January 24, 2005 | Architecture Proposal

2. ● General Purpose chip that performs a wide variety of functions – Differencer – Integrator – Leaky Integrator – First-Order Delay Network – Audio Comb – Etc ● Significance – Applications in all fields of DSP (digital signal processing) – Replaces commonly used algorithms based on the input coefficients – Help increase efficiency of DSP circuit design via re-use Architecture Proposal Stage 2 | January 24, 2005 | Architecture Proposal

3. Final Algorithm [1] ● H(z ) = (1 − c 1 z −N ) x b 0 + b 1 z −1 + b 2 z −2 1/a 0 − a 1 z −1 − a 2 z −2 Stage 2 | January 24, 2005 | Architecture Proposal

4. Initial Block Diagram

5. Floating Point Modification Stage 2 | January 24, 2005 | Architecture Proposal

6. Floating Point Addition [2] Stage 2 | January 24, 2005 | Architecture Proposal

7. Refined Components Stage 2 | January 24, 2005 | Architecture Proposal FP Multiplier Floating Point Adder Detail

8. Benchmark Graphs

9. Matlab Code function output = swiss(z,a,b,c,N) %a DSP "swiss army knife" n = [0 1 zeros(1,98)]; max = length(z); t = [-0.5: 2*0.5/max: 0.5-2*0.5/max]; Hz = (1-c*z.^-N).* ((b(1)+b(2)*z.^-1+b(3)*z.^-2)./... ( (1/a(1))-a(2)*z.^-1 - a(3)*z.^-2)); plot(t,(abs(fftshift(Hz)).*10)-12.5,'b'); output = real(fftshift(Hz).*10)-12.5; Stage 2 | January 24, 2005 | Architecture Proposal

10. Benchmark Graphs

11. Matlab Results a 0 = a 1 = 1 ; a 2 = 0 b 0 = 1/N ; b 1 = b 2 = 0 c 1 = 1 ; N = 8 Stage 2 | January 24, 2005 | Architecture Proposal

12. Matlab Results a 0 = 1 ; a 1 = 0 ; a 2 = 0 b 0 = 1 ; b 1 = -1 ; b 2 = 0 c 1 = 0 Stage 2 | January 24, 2005 | Architecture Proposal

13. Matlab Results a 0 = a 1 = 1 ; a 2 = 0 b 0 = 1 ; b 1 = 0 ; b 2 = 0 c 1 = 0 Stage 2 | January 24, 2005 | Architecture Proposal

14. Matlab Results a 0 = 1 ; a 1 = 1 - α ; a 2 = 0 b 0 = α ; b 1 = 0 ; b 2 = 0 c 1 = 0 ; Stage 2 | January 24, 2005 | Architecture Proposal

15. Verilog Code module swiss (output reg [11:0] hz, input [11:0] z, // in floating point form i.e. S*b^E [11]sign/[10:6]E/[5:0]S input [4:0] N, // assumption that N is a positive integer input [1:0] c1, b0, b1, b2, a0, a1, a2); // bit1 for sign, bit0 for value // assuming all inputs except z are -1, 0, 1 // currently non-renormalized floating point numbers Stage 2 | January 24, 2005 | Architecture Proposal

16. Verilog Code reg [11:0] zN; // create an intermediate floating point variable reg [11:0] one = 12'b000000000001; reg [11:0] num = 12'b000000000000; reg [11:0] numtemp = 12'b000000000000; reg [11:0] den = 12'b000000000000; reg [11:0] dentemp1 =12'b000000000000; reg [11:0] dentemp2 =12'b000000000000; reg [11:0] biquad = 12'b000000000000; reg [4:0] diff; reg [3:0] i; always@(z, N, c1, b0, b1, b2, a0, a1, a2) begin zN = z;// set intermediate variable zN to value of input z Stage 2 | January 24, 2005 | Architecture Proposal

17. Verilog Code // performing operation z^N if (N==5'b00000) zN = 12'b000000000001; else begin for(i=4'b0001; i<N; i=i+1) begin zN[5:0] = zN[5:0] * z[5:0]; zN[10:6] = zN[10:6] + z[10:6] - 5'b01111; if(zN[11] == 1 && z[11] == 0) zN[11] = 1; else if(zN[11] == 0 && z[11] == 1) zN[11] = 1; else zN[11] = 0; end end // else: !if(N==5'b00000) Stage 2 | January 24, 2005 | Architecture Proposal

18. Verilog Code // performing operation c1/z^N (or c1*z^-N) if (c1[0] == 0) zN = 12'b000000000000; else begin zN[5:0] = 6'b000001 / zN[5:0]; zN[10:6] = -zN[10:6] + 5'b01111; if(c1[1] == 1 && zN[11] == 0) zN[11] = 1; else if(c1[1] == 0 && zN[11] == 1) zN[11] = 1; else zN[11] = 0; end // else: !if(c1[0] == 0) Stage 2 | January 24, 2005 | Architecture Proposal

19. Verilog Code // performing operation 1 - c1*z^-N // zN = 1 - c1*z^-N (comb filter) zN[11]=~zN[11]; if(one[10:6]>zN[10:6]) begin diff[4:0]=one[10:6]-zN[10:6]; zN[5:0] = zN[5:0]>>diff; end else if(zN[10:6]>one[10:6]) begin diff[4:0]=zN[10:6]-one[10:6]; one[5:0] = one[5:0]>>diff; end zN[5:0]=zN[5:0]+one[5:0]; one[11:0] = 12'b000000000001; Stage 2 | January 24, 2005 | Architecture Proposal

20. Verilog Code // performing b1/z (or b1*z^-1) if (b1[0] == 0) num[11:0] = 12'b000000000000; else begin num[5:0] = 6'b000001 / z[5:0]; num[10:6] = -z[10:6] + 5'b01111; if(b1[1] == 1 && num[11] == 0) num[11] = 1; else if(b1[1] == 0 && num[11] == 1) num[11] = 1; else num[11] = 0; end // else: !if(b1[0] == 0) (...etc...) Stage 2 | January 24, 2005 | Architecture Proposal

21. Verilog Test Bench module test_swiss (output n,z,b0,b1,b2,a0,a1,a2 input hz); initial begin $moniter($time,, "n=%b z=%b b0=%b b1=%b b2=%b a0=%b a1=%b a2=%b hz%b" n,z,b0,b1,b2,a0,a1,a2,hz); #10/// (set input values here) #10/// Inputs not well defined, so no useful comparison to matlab results yet #10 end // initial begin endmodule // test_swiss Stage 2 | January 24, 2005 | Architecture Proposal

22. Proposal Estimates Stage 2 | January 24, 2005 | Architecture Proposal Waiting to re-calculate based on input definitions and the bit-width of the floating point numbers (12-point FP gives similar estimates as above)

23. Marketing ● DSP – Communications ● Wireless & standard – Video ● Noise reduction – Audio ● Basic building block of acoustic audio effects such as acoustic echo simulation and plucked instrument synthesis ● May require floating point accuracy to be useful Stage 2 | January 24, 2005 | Architecture Proposal

24. Status ● Research (restarted) ● Transistor count (awaiting defined inputs) ● Block Diagram (altered for floating point) ● Verilog description (50%) ● Layout (0%) ➢ To Be Done ➢ Define inputs and FP bit-width ➢ Finalize Transistor count ➢ Refine block diagram ➢ Verilog / Layout / Verification Stage 2 | January 24, 2005 | Architecture Proposal

25. Design Decisions ● Move to floating point architecture ● Memory / Registers not included pending bit- width Stage 2 | January 24, 2005 | Architecture Proposal

26. Problems & Questions ● Benchmark inputs not well defined ● Pushing the transistor count cap ● Hardware implementation of x -n and -1 not obvious (solved by floating point) ● Circuit may be a 'novelty' at only 8 bits (solved by floating point) Stage 2 | January 24, 2005 | Architecture Proposal

27. References ● [1] http://www.ecpe.vt.edu/fac_support/DSPCL/docs/SPMag04.pdfhttp://www.ecpe.vt.edu/fac_support/DSPCL/docs/SPMag04.pdf ● [2] http://www.cse.psu.edu/~cg575/lectures/cse575-fpops.pdfhttp://www.cse.psu.edu/~cg575/lectures/cse575-fpops.pdf