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Convolution

The convolution of two signals $ x$ and $ y$ in $ {\bf C}^N$ may be denoted `` $ x\circledast y$'' and defined by

$\displaystyle \zbox {(x\circledast y)_n \isdef \sum_{m=0}^{N-1}x(m) y(n-m)}
$

Note that this is circular convolution (or ``cyclic'' convolution).7.3 The importance of convolution in linear systems theory is discussed in §8.3



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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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