Fourier Transform (FT) and Inverse Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search


Fourier Transform (FT) and Inverse

The Fourier transform of a signal $ x(t)\in{\bf C}$, $ t\in(-\infty,\infty)$, is defined as

$\displaystyle X(\omega) \isdef \int_{-\infty}^\infty x(t) e^{-j\omega t} dt, \protect$ (B.1)

and its inverse is given by

$\displaystyle x(t) = \frac{1}{2\pi}\int_{-\infty}^\infty X(\omega) e^{j\omega t} d\omega. \protect$ (B.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
CCRMA  [Automatic-links disclaimer]