95-1 Under-Graduate Project Paper Reading Presentation Speaker: 陳柏偉 許名宏 Advise: Prof. An-Yeu Wu Mentor: 陳彥良 Date: 2006/10/25

Outline Radix-22 Algorithm Radix-22 Structure Procedure Matlab Simulation

Radix-22 Algorithm Define of DFT of size N: which

16 Points FFT BFI BFI BFII -1 ? -1

Time Domain to Frequency Domain Bit reverse x(3) => X(12) 00 1 1 11 0 0 k3 k2k1 …

Twiddle Factor

Twiddle Factor for 64 Points & More k1=0,1 k2=0,1 Bit reverse x(16) => X(2) 010000 000010 Also apply for 4n points

Radix-22 Structure

BF2i & BF2ii

First N/2-1 Cycles

N/2th ~Nth Cycles

Last N Cycles

Matlab Simulation Array reg N-N/4 Clk => binary function

Array Register 1024 = 210 “10” registers reg512(1:512)=0;

BF2i & BF2ii Function if t==0 y(1:2)=[a b]; end if t==1 & s==1 y(1:2)=[a+(b) a-(b)]; if t==1 & s==0 y(1:2)=[a+(b*-i) a-(b*-i)];

Clock binclk=dec2binvec(clk,bit);

Circuit Simulation wire1 = BF1(reg128, input, clk7); reg128 =wire12; wire2=BF2(reg64, wire11, clk7, clk6); reg64=wire22; output=wire21* W1(from3N/4);

Result – Design & Correct(1/2)

Result – Design & Correct(2/2)

Conclusion Radix-22 structure and algorithm Radix-22 SDF FFT architecture Matlab simulation 1024 points FFT

Future work Verilog code Synthesis Other architecture

Reference [1] S. He and M. Torkelson. A new approach to pipeline FFT processor. Proceedings of IPPS’96, 1996 [2] discrete-time signal process 2nd edition A.V. Oppenheim R.W Schafer For matlab http://webclass.ncu.edu.tw/~junwu/index.html http://www.cs.nthu.edu.tw/~jang/mlbook/