1. Reconfigurable FFT architecture
Saba Zia
Dec 17,2008

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

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