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Discrete Fourier Transform (DFT)

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(1)

Discrete Fourier Transform

(DFT)

(2)

Inverse DFT

Transform Fourier coefficients to time domain samples

DFT Transform time domain samples to Fourier coefficients

(3)
(4)
(5)
(6)

n=16

(7)

n=32

(8)

n=16

(9)

Fast Fourier Transform

(FFT)

(10)
(11)
(12)

Reduction of effort by half!

(13)
(14)

Reduction of effort by half!

(15)

Order 8-DFT reduced to 2 order 4-DFTs

(16)

2 order 4-DFTs reduced to 4 oder 2-DFTs

(17)

4 order 2-DFTs reduced to 8 oder 1-DFTs: FFT.

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