14.4. Summary

Of all the mathematical algorithms discussed in this book, the FFT is my favorite. No other algorithm combines mathematical beauty with hard, practical utility. It is the most crucial algorithm in the field of signal processing, and the better you understand it, the faster your systems will execute.

The first part of this chapter discussed the topic of frequency analysis, focusing on how to remove noise from a song using digital remastering. The goal is to sample a continuous time-domain signal, x(t), to produce a time-domain sequence, x[n]. The discrete Fourier transform (DFT) transforms x[n] into a sequence containing frequency components, X[k], and you can remove noise by setting unwanted frequencies to zero. Then the inverse DFT transforms the frequency components back into a time-domain signal.