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VLSI Implementation for Fast Fourier Transform: A Review of Methods

Explore various FFT implementation methods discussing speed, area, control, and design considerations. Compare radix types and decomposition strategies. Analyze architectures for efficient VLSI processing in FFT applications.

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VLSI Implementation for Fast Fourier Transform: A Review of Methods

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  1. FFT VLSI Implementation VLSI Signal Processing 台灣大學電機系 吳安宇 • Shousheng He and Mats Torkelson, A new approach to pipeline FFT processor. IEEE Proc. Of IPPS, P766-770, 1996. • E. Bidet, D. Castelain, C. Joanblanq, and P. Senn, A fast single-chip implementation of 8192 complex point FFT. IEEE J. Solid-State Circuits, P300-305, March 1995

  2. FFT Review

  3. Implementation--- Two Extreme Method Slow ----------------- Speed ----------------- Fast Small ------------------Area------------------- Large Complicated  ------------ Control --------------- Simple

  4. Design Consideration • System Requirement • e.g., speed, area,power … • Trade-off in these two cases, we need • More Processing Elements (PE’s) • Better Processing Element Utilization Rate • Better Control Scheme

  5. FFT Processor--- Block Diagram

  6. Some Current Themes Radix-2 Multi-path Delay Commutator. ( N = 16 ) Radix-2 Single-path Delay Feedback. ( N = 16 )

  7. Radix-4 Single-path Delay Commutator. ( N = 256 ) Radix-4 Multi-path Delay Commutator. ( N = 256 ) Radix-4 Single-path Delay Feedback. ( N = 256 ) Some Current Themes (cont.)

  8. Distinctive merit of the above • The delay-feedback are more efficient than delay-commutator in terms of memory utilization • Radix-4 has higher multiplier utilization ,however,Radix-2 has simpler BF which are better utilized

  9. Comparison Radix / Speed Low  ----------------------------------- High Processing Ability / Unit Low  ----------------------------------- High Control Theme Simple ----------------------------------- Complex Combine the advantages  Further decompose high radix PE

  10. Decompose Method (1) • Simply ‘‘reuse’’ the repeated micro unit A radix-4 PE

  11. Decompose Method (2) • From algorithm level Applying 3 index: n=<n1*N/2 + n2*N/4 + n3>N k=<k1 + 2k2 + 4k3>N where n1,n2={0,1} ;n3={0~N/4-1} Summation of n1

  12. Decompose Method (2) cont. Summation of n2 Only real-imaginary swapping & sign inversion

  13. Graphical Explanation (N=16) Trivial multiplication

  14. Graphical Explanation (cont.) • The Eqs are equivalent to the operations below

  15. Circuit of BF2I First N/2 cycles Xr(n) Zr(n+N/2) Xi(n) Zi(n+N/2) Xr(n+N/2) Zr(n) Xi(n+N/2) Zi(n) Second N/2 cycles

  16. Circuit of BF2II Xr(n) Zr(n+N/2) Xi(n) Zi(n+N/2) Xr(n+N/2) Zr(n) Xi(n+N/2) Zi(n) Swap Re&Im and sign inversion

  17. Radix-22 Single-path Delay Feedback FFT architecture using the above technique, for N=256 Compare with original architecture, for N=256

  18. Structural advantage 2 • Radix-2 has the same complexity as radix-4,but still retain radix-2 BF structure • The stage has non-trivial multiplication • Control is simple; synchronization controller address counter for W n

  19. Conclusions • FFT Applications: Radar Signal Processing, Fast convolution, Spectrum Estimation, OFDM-based Modulation/demodulations • Efficient VLSI architectures (parallel processing) are required for real-time processing. • However, most systems still employ DSP processors (e.g., TI C3x/C5x) for computations (fast algorithms like DIT and DIF FFT). • VLIW (Very Long-length Instruction Word)-based processors (TI C6x) need new programming skills to utilize the two parallel MAC units.

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