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Autocorrelation

The cross-correlation of a signal with itself gives the autocorrelation function of that signal:

$\displaystyle r_{x}(l) \isdef r_{xx}(l) = E\{\overline{x(n)}x(n+l)\}$ (C.25)

Note that the autocorrelation function is Hermitian:

$\displaystyle r_x(-l) = \overline{r_x(l)}
$

When $ x$ is real, its autocorrelation is symmetric. More specifically, it is real and even.


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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2014-06-03 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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