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Wikipedia gives the cross-correlation as

$$ \begin{align*} (f \star g)[n] = \sum^{\infty}_{m = -\infty} f^{*}[m] g[n+m] \end{align*} $$

MATLAB's documentation gives xcorr(x, y) as

$$ \begin{align*} R_{xy}[n] = E(x[n+m]y^{*}[m]) \end{align*} $$ where $E$ is the evaluation function and I have switched $m$ and $n$ so it's consistent with Wikipedia's notation.

They're obviously opposite with respect to one another. If Wikipedia's definition is correct, why did MATLAB implement their function to be the opposite of the mathematical definition?

Am I missing something here? Because this difference just caused me a lot of pain while working on a project.

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  • $\begingroup$ Aren't these just the complex conjugates of each other? $\endgroup$ Commented Apr 29, 2012 at 5:22
  • $\begingroup$ Can you explain further? How are they complex conjugates? $\endgroup$ Commented Apr 29, 2012 at 6:13
  • $\begingroup$ Well, If understood you correctly, the only difference is: $$(f \star g)_{matlab}$$ = $$(g \star f)_{wiki}$$ $\endgroup$ Commented Apr 29, 2012 at 7:56
  • $\begingroup$ Yes, which tripped me up for a while. Just wondering if this is just an annoying "feature", or am I missing out on some critical reason for MATLAB's method of implementation. $\endgroup$ Commented Apr 29, 2012 at 8:23

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It's just a matter of notation - similar to the definition of the Fourier Series (does one include $2\pi$ ? ). All properties of the cross correlation stay the same.

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