Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

Why a DFT is usually called an FFT in practice

Practical implementations of the DFT are usually based on one of the Cooley-Tukey ``Fast Fourier Transform'' (FFT) algorithms [17].8.1 For this reason, the matlab DFT function is called `fft', and the actual algorithm used depends primarily on the transform length $ N$ .8.2 The fastest FFT algorithms generally occur when $ N$ is a power of 2. In practical audio signal processing, we routinely zero-pad our FFT input buffers to the next power of 2 in length (thereby interpolating our spectra somewhat) in order to enjoy the power-of-2 speed advantage. Finer spectral sampling is a typically welcome side benefit of increasing $ N$ to the next power of 2. Appendix A provides a short overview of some of the better known FFT algorithms, and some pointers to literature and online resources.


Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

[How to cite this work]  [Order a printed hardcopy]  [Comment on this page via email]

``Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition'', by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8
Copyright © 2024-04-02 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA