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I Independence of variables in Convolution

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  1. May 27, 2017 #1
    Given a convolution:
    \begin{equation}
    \begin{split}
    g(x) * h(x) &\doteq \int_{-\infty}^{\infty} g(z) h(x-z) dz
    \end{split}
    \end{equation}

    Do ##z## and ##x## have to be independent? For example, can one set ##x=z+y## such that:
    \begin{equation}
    \begin{split}
    \int_{-\infty}^{\infty} g(z) h(x-z) dz&=\int_{-\infty}^{\infty} g(z) h(y) dz
    \end{split}
    \end{equation}
     
  2. jcsd
  3. May 27, 2017 #2

    FactChecker

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    Science Advisor
    Gold Member

    The variable z is a temporary variable for the integral. You can not make x depend on it.
     
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