Fast Fourier Transform Generator ChiaWei Chen ADSP 20130510

Fast Fourier Transform Generator Chia-Wei Chen ADSP 2013/05/10 1

Overview DFT FFT 2

Outline • 1. History of FT/FFT • 2. FFT Algorithm • 3. FFT Hardware • 4. FFT Generator 3

History of FT • Joseph Fourier 1768 -1830 1822 4

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History of FFT • Cooley & Tukey 1965 • Gauss 1777 -1855 1805 6

History of FFT 1805: Fast Algorithm 1822: FT DFT 1965: FFT 7

Outline • 1. History of DFT/FFT • 2. FFT Algorithm • 3. FFT Hardware • 4. FFT Generator 8

Radix-2 FFT 9

Radix-2 8 -point FFT 10

Radix-23 FFT 11

Radix-23 8 -point FFT -j -j -j 12

Comparison • Complexity • DFT > Radix-23 DFT • Performance • Radix-23 > Radix-2 > DFT Radix-23 -j -j -j 13

Outline • 1. History of DFT/FFT • 2. FFT Algorithm • 3. FFT Hardware • 4. FFT Generator 14

Single-Path Delay Feedback (SDF) Radix-2 BF BF BF 15

Single-Path Delay Feedback (SDF) BF 16

• For the students of GICE • Course: Digital Signal Processing • Prof. Pei • Radix-2^3 • Complexity Performance • For the students of GIEE • Course: Digital Signal Processing in VLSI Design • Prof. Chien • Schedule Table Animations 17

Outline • 1. History of DFT/FFT • 2. FFT Algorithm • 3. FFT Hardware • 4. FFT Generator 18

FFT Generator • Matlab • C++ • Verilog • FPGA FFT or IFFT Length SQNR Operation speed Antenna number FFT/IFFT Generator Verilog file Test bench 19

Flowchart 20

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Target: SQNR=55 d. B 22

Demonstration 23

Thank You! 24