A DFT is a "Discrete Fourier Transform". An FFT is a "Fast Fourier Transform". An FFT is a DFT, but is much faster for calculations. The whole point of the FFT is speed in calculating a DFT.

An 8 Input Butterfly

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Here is an example of an 8 input butterfly:

Butterfly 8 Input Example

An The 8 input butterfly diagram has 12 2-input butterflies and thus 12*2 = 24 multiplies.

N Log N = 8 Log (8) = 24. A straight DFT has N*N multiplies, or 8*8 = 64 multiplies. That's a pretty good savings for a small sample. The savings are over 100 times for N = 1024, and this increases as the number of samples increases.


You can keep expanding the butterfly by the same procedure.

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