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Reconfigurable FFT architecture

Reconfigurable FFT architecture. Saba Zia Dec 24,2008. Specifications. 64 point FFT 32 butterfly operations 14 points 2’s complement representation DIF radix-2 LUT for twiddle factors Rounding off for arithmetic gain. Fast Fourier Transform - Mathematics. -1. -1. - 1. - 1. j. j.

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Reconfigurable FFT architecture

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  1. Reconfigurable FFT architecture Saba Zia Dec 24,2008

  2. Specifications 64 point FFT 32 butterfly operations 14 points 2’s complement representation DIF radix-2 LUT for twiddle factors Rounding off for arithmetic gain

  3. Fast Fourier Transform - Mathematics

  4. -1 -1 -1 -1 j j W0 -j -j W1 Time Domain Samples Frequency Domain Outputs -1 -1 W2 W3 W4 W5 W6 W7 Simplified 8-point FFT

  5. Periodicity of twiddle factors

  6. DIT and DIF

  7. 8 point radix 2 FFT - DIF

  8. Algorithm Number of points = N = 64 Total stages = log2N = 6 Total butterflies in each stage = N/2 = 32 Twiddle factor to retrieve in each stage = N/2 Optimal retrieval of twiddle factor in each stage = 2(total stages – stage number) First Data index = i (where i = 0 to N/2) Second Data index = 2(total stages – stage number) + i Twiddle Factor index = j = 0 to 2(total stages – stage number) - i

  9. State Machine

  10. Parallel 768-Point Split-Radix FFT Reference: Dillon Engineering Inc

  11. Split radix structure 64-point FFT 64-point FFT 4- point FFT 4- point reorder 64-point FFT 64-point FFT

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