Fast Fourier Transforms (FFT) Next  |  Prev  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

Fast Fourier Transform (FFT) Algorithms

The term fast Fourier transform (FFT) refers to an efficient implementation of the discrete Fourier transform (DFT) for highly compositeA.1 transform lengths $ N$. When computing the DFT as a set of $ N$ inner products of length $ N$ each, the computational complexity is $ {\cal O}(N^2)$. When $ N$ is an integer power of 2, a Cooley-Tukey FFT algorithm delivers complexity $ {\cal O}(N\lg N)$, where $ \lg N$ denotes the log-base-2 of $ N$. Such FFT algorithms were evidently first used by Gauss in 1805 [29] and rediscovered in the 1960s by Cooley and Tukey [14].

Pointers to FFT software are given in §A.7.A.2

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[How to cite this work] [Order a printed hardcopy]

``Mathematics of the Discrete Fourier Transform (DFT), with Music and Audio Applications'', by Julius O. Smith III, W3K Publishing, 2003, ISBN 0-9745607-0-7.
Copyright © 2007-02-02 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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