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A DFT and FFT TUTORIAL

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.

DFT and FFT

FFT

Outline For Learning About The DFT and FFT

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Here is an outline of the steps used to explain both the DFT and FFT.

  1. First the DFT will be explained. This is the vital first step, since an FFT is a DFT and there are, therefore, basic concepts in common with both. Learning this first will make understanding the FFT easier.
  2. Once you understand the basic concepts of a DFT, the FFT will be explained. This is broken into several steps.
  3. The "Danielson-Lanczos Lemma" will be explained, which is the first step to understanding the FFT.
  4. The "twiddle factor" will be explained, which is another key to understanding the FFT.
  5. The "Butterfly Diagram" will be explained. The Butterfly is an FFT in diagram form. It's the final step of this tutorial and builds on the prior concepts.
  6. Several examples will be given along with the basic concepts above.
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