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Paper Reading - A New Approach to Pipeline FFT Processor

Paper Reading - A New Approach to Pipeline FFT Processor. Presenter: Chia-Hsin Chen, Yen-Chi Lee Mentor: Chenjo Instructor: Andy Wu. Outline. What’s FFT FFT on Hardware Comparison C/C++ Sim Further Study Reference. What’s DFT.

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Paper Reading - A New Approach to Pipeline FFT Processor

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  1. Paper Reading -A New Approach to Pipeline FFT Processor Presenter: Chia-Hsin Chen, Yen-Chi Lee Mentor: Chenjo Instructor: Andy Wu

  2. Outline • What’s FFT • FFT on Hardware • Comparison • C/C++ Sim • Further Study • Reference Owen, Lee

  3. What’s DFT • The Fourier transform of discrete-time signals continuous function • Sample X(ω) at equal spaced frequencies discrete function this is called the discrete Fourier transform (DFT) of x(n) Owen, Lee

  4. What’s FFT • An efficient algorithm computes DFT • Twiddle Factor: Owen, Lee

  5. What’s FFT (cont.) • Direct computation • N2 multiplication • N(N – 1) addition • FFT • Symmetry: • Periodicity: Owen, Lee

  6. Divide-and-Conquer • Simple divide case: • N = LM (for N points) • n=l+mL, k=Mp+q • Apply 2-dimensional index map where Owen, Lee

  7. Two Dimensional Sequence Owen, Lee

  8. Computations decrease Comparison Owen, Lee

  9. Radix • Let N=r1r2r3…rv • For special case N=rv • r is called the radix • r = 2 Owen, Lee

  10. Radix-2 Butterfly • DIT • DIF Owen, Lee

  11. Review of FFT approach • A divide and conquer approach • Radix-2 Multi-path Delay Commutator • Radix-2 Single-path Delay Feedback • Radix-4 Single-path Delay Feedback Owen, Lee

  12. Review (cont.) • Radix-4 Multi-path Delay Commutator • Radix-4 Single-path Delay Commutator Owen, Lee

  13. Radix-22 DIF Algorithm • Proposed by S. He and M. Torkelson • Applying a 3-dimensional linear index map Owen, Lee

  14. Radix-22 DIF Algorithm (cont.) Owen, Lee

  15. Radix-22 DIF Algorithm (cont.) Owen, Lee

  16. Butterfly with Decomposed Twiddle Factors Owen, Lee

  17. Relation Between Radix-4 & Radix-22 • Combined Radix-4 with Radix-2 Owen, Lee

  18. R22SDF Pipeline FFT • Example: N=256 Owen, Lee

  19. Comparison Owen, Lee

  20. C/C++ Simulation • Complex class • BF2i、BF2ii • DelayReg • ComputeW • DFT • FFT4->FFT16->FFT64->FFT256->FFTn Owen, Lee

  21. C/C++ Sim (cont.) Owen, Lee

  22. Further Study • R23SDF • Proposed by S. He and M. Torkelson Owen, Lee

  23. Further Study (cont.) • R24SDF • Proposed by J. OH and M. LIM Owen, Lee

  24. CORDIC • COordinate Rotation DIgital Computer • An iterative arithmetic algorithm introduced by Volder in 1956 • Can handle many elementary functions, such as trigonometric, exponential, and logarithm with only shift-and-add arithmetic Owen, Lee

  25. References • S. He and M. Torkelson. “A new approach to pipeline FFT processor.” IEEE Proceedings of IPPS ’96. • S. He and M. Torkelson. “Designing Pipeline FFT Processor for OFDM (de)Modulation.” ISSSE, pp. 257-262, Sept. 1998. • J. Y. Oh and M. S. Lim. “New Radix-2 to the 4th Power Pipeline FFT Processor.” IEICE Trans. Electron., Vol.E88-C, No.8 Aug. 2005 • E. E. Swartzlander, W. K. W. Young, and S. J. Joseph. “A radix 4 delay commutator for fast Fourier transform processor implementation.” IEEE J. Solid-State Circuits, SC-19(5):702-709, Oct. 1984. • C. D. Thompson. “Fourier transform in VLSI.” IEEE Trans. Comput., C-32(11):1047-1057, Nov.1983. • Y. Jung, Y. Tak, J. Kim, J. Park, D. Kim, and H. Park. “Efficient FFT Algorithm for OFDM Modulation.” Proceedings of IEEE Region 10 International Conference on Electrical and Electronic Technology. Vol.2 pp.676-678, 2001. • A. M. Despain. “Very Fast Fourier Transform Algorithms Hardware for Implementation.” IEEE Trans. on Computers, Vol. c-28, No. 5, May 1979 • A. –Y. Wu. “CORDIC.” Slides of Advanced VLSI • Y. H. Hu. “CORDIC-based VLSI architectures for digital signal processing.” IEEE Signal Processing Magazine. Pp. 16-35. July 1992 • J. G. Proakis. D. G. Manolakis. “Digital signal processing” 3rd edition, Prentice Hall Owen, Lee

  26. Thanks for Your Attention Q & A ? Owen, Lee

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