Reconfigurable FFT architecture Saba Zia Dec 17,2008

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

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

Periodicity of twiddle factors

DIT and DIF

8 point radix 2 FFT - DIF

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

State Machine

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