
Chapter 8
The Fast Fourier Transform
8.1 Theory
T
HE Fast Fourier Transform (FFT) is just what the name says it is: a fast way for com-
puters to calculate the Fourier transform, specifically the Discrete Fourier Transform
(DFT). The introduction of the FFT algorithm by Cooley and Tukey in 1965 revolution-
ized signal processing and has had an enormous effect on engineering and applied science
in general [1]. This chapter is by no means a treatise on the FFT. Despite the fact that we
will only cover a few of the major points, this is still a long chapter, but we encourage you
to read it completely. For more details about the FFT, see [2, 4, 69].
Having