Digital Signal Processing 101

CHAPTER 10Discrete and Fast Fourier Transforms (DFT, FFT)

You have likely heard the term FFT. In this chapter, we discuss the discrete Fourier transform, or DFT, and its more popular cousin, the fast Fourier transform, or FFT. We again try to approach this topic intuitively, although a bit of math is unavoidable.

The key is to understand the DFT operation. The FFT is simply a highly optimized implementation of the DFT. They both produce identical results. While the implementation of the FFT is interesting, unless you are actually building it, you don’t really need to know the details. Because the FFT is such a basic building block in DSP, many implementations are already available.

So just what is the DFT? To start with, the DFT is simply a transform. ...