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What's the difference between convolution and crosscorrelation?

  1. May 1, 2013 #1
    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
     
  2. jcsd
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