1. A New Approach to Pipeline FFT Processor
Speaker: Group B3 B 徐誠羿
B 高翊軒
Adviser: Prof. An-Yeu Wu
Date:

2. Outline DFT FFT Previous pipeline FFT processor architectures
New FFT processor radix-22
Comparison
New FFT processor Radix-23
Conclusion
Simulation
References

3. DFT
Definition of Discrete Fourier Transform and Inverse DFT.

4. FFT
An algorithm which computes DFT. A method of multiplying Discrete Fourier Transform.
Concept: Divide and conquer.
points only (using butterfly structure)

5. Previous Pipeline FFT Processor Architectures
R2MDC( Radix-2 Multi-path Delay Commutator )

6. R4MDC(Radix-4 Multi-path Delay Commutator)
R4SDC(Radix-4 Single-path Delay Commutator)

7. Radix-2 (Radix-2 Single-path Delay Feedback)
DIT (bit reverse->normal)
DIF (normal->bit reverse)

8. Radix-2(cont.)

9. Radix-4(Radix-4 Single-path Delay Feedback)
multipliers

10. Ideal Architecture Minimum multipliers Minimum adders
Minimum memory size

11. New FFT processor radix-22􀂙
It has the same multiplicative complexity as radix-4 algorithm, but retain butterfly structure of radix-2 algorithm.
For length-N DFT compution, it requires:
complex multipliers
complex data memory
-> minimum in the above processor

12. Derivation

13. Point Flow

14. BF Picture

15. Radix-22

16. BF2i and BF2ii Structure

17. Hardware Comparison multiplier Memory size R2MDC 2( ) R2SDF N-1 R4 SDF
2( )
R2SDF
N-1
R4 SDF
R4MDC
3( )
R4SDC
2N-2
R SDF
adder 4 8 3

18. Simulation
Input x(n) = n + n*j , n=[0,63]

19. Simulation(Comparison)
Compare with MATLAB FFT

20. Conclusion Radix-22;multiplicitive complexity => Radix-4.
butterfly structure => Radix-2.
Use single delay feedback.
Using fixed points arithmetic and a complex array multiplier.
An ideal architecture for VLSI implementation of pipeline FFT processors.

21. New FFT Processor Radix-23(1/4)
It has the same multiplicative complexity as radix-8 algorithm, but retain butterfly structure of radix-2 algorithm.
Faster and smaller than radix-2 and radix-22 .
Combine radix-8 and radix-2.
multiplier only.

22. New FFT Processor Radix-23(2/4)

23. New FFT Processor Radix-23(3/4)

24. New FFT Processor Radix-23 (4/4)

25. Reference
Alan V.Oppenheim, Ronald W.Schafer, “Discrete-time signal processing” 2nd edition.
Shousheng He and Trkelson, M.,”A new approach to pipeline FFT processor,” Procesdings of IPPS’96, April 1996, pp
Signals and system. Chen..
Signals and system. Haykin.1st edition.
OFDM Radix 23 website .hsu.cc.orz
Discrete Signal processing.4th ed

26. Thank you 