What's the difference between convolution and crosscorrelation?(adsbygoogle = window.adsbygoogle || []).push({});

I read the answer below, but I don't know enough math to understand it.

Could someone clarify it for me, please?

"The meaning is quite different. To see why in a simple setting, consider [itex]X[/itex] and [itex]Y[/itex] independent integer valued random variables with respective distributions [itex]p=(p_n)_n[/itex] and [itex]q=(q_n)_n[/itex].

The convolution [itex]p\ast q[/itex] is the distribution [itex]s=(s_n)_n[/itex] defined by [itex]s_n=\sum\limits_kp_kq_{n-k}=P[X+Y=n][/itex] for every [itex]n[/itex]. Thus, [itex]p\ast q[/itex] is the distribution of [itex]X+Y[/itex].

The cross-correlation [itex]p\circ q[/itex] is the distribution [itex]c=(c_n)_n[/itex] defined by [itex]c_n=\sum\limits_kp_kq_{n+k}=P[Y-X=n][/itex] for every [itex]n[/itex]. Thus, [itex]p\circ q[/itex] is the distribution of $Y-X$.

To sum up, [itex]\ast[/itex]acts as an addition while [itex]\circ[/itex] acts as a difference."

http://math.stackexchange.com/quest...onvolution-and-crosscorrelation/353309#353309

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# What's the difference between convolution and crosscorrelation?

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