# What's the difference between convolution and crosscorrelation?

1. May 1, 2013

### JonMuchnick

What's the difference between convolution and crosscorrelation?

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 $X$ and $Y$ independent integer valued random variables with respective distributions $p=(p_n)_n$ and $q=(q_n)_n$.

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

To sum up, $\ast$ acts as an addition while $\circ$ acts as a difference."
http://math.stackexchange.com/quest...onvolution-and-crosscorrelation/353309#353309