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.

The Goal of This Tutorial

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The goal of this tutorial is to show how to take a discretely sampled wave, usually from nature, and convert it to the frequency domain by using an FFT. An FFT is a DFT of a particular form. An FFT is simply a fast way of calculating a DFT. Before explaining the FFT I explain the DFT. I do this for three reasons.

  1. A DFT is much simpler to understand mathematically, which is better for learning.
  2. Once you understand what the terms of a DFT mean, they apply to the FFT, so you are learning the FFT too.
  3. You will gain an appreciation for what the FFT accomplishes, because it is derived from the DFT and the only purpose of the complex math of an FFT is to speed up the DFT calculation. It's purely about speedy number crunching and changes none of the fundamentals.
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