# I Independence of variables in Convolution

Tags:
1. May 27, 2017

### redtree

Given a convolution:

\begin{split}
g(x) * h(x) &\doteq \int_{-\infty}^{\infty} g(z) h(x-z) dz
\end{split}

Do $z$ and $x$ have to be independent? For example, can one set $x=z+y$ such that:

\begin{split}
\int_{-\infty}^{\infty} g(z) h(x-z) dz&=\int_{-\infty}^{\infty} g(z) h(y) dz
\end{split}

2. May 27, 2017

### FactChecker

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