1. 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

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

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

4. 16 Points FFT
BFI
BFI
BFII -1 ? -1

5. Time Domain to Frequency Domain
Bit reverse
x(3) => X(12)
k3 k2k1 …

6. Twiddle Factor

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

8. Radix-22 Structure

9. BF2i & BF2ii

10. First N/2-1 Cycles

11. N/2th ~Nth Cycles

12. Last N Cycles

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

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

15. 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)];

16. Clock
binclk=dec2binvec(clk,bit);

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

18. Result – Design & Correct(1/2)

19. Result – Design & Correct(2/2)

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

21. Future work
Verilog code
Synthesis
Other architecture

22. 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