The fast Fourier transform (FFT) represents one of the most important advancements in scientific and engineering computing of the last century. Until now, however, treatments of algorithmic aspects of FFT have been either brief, cryptic, intimidating, or not published in the open literature. Inside the FFT Black Box takes a unified and systematic approach that brings the numerous and varied ideas together into a common notational framework. It bridges the gap between textbooks and the literature on serial and parallel FFT algorithms and provides a modern, self-contained guide for learning the FFT and the multitude of ideas and computing techniques it employs.