# Proof of the Commutativity property of LTI systems (ECE301)

Given: $y[n]=x[n]*h[n]=\sum_{k=-\infty}^{\infty}(x[k]h[n-k])$

1. $x[n]*h[n]=\sum_{k=-\infty}^{\infty}(x[k]h[n-k])$
2. $k'=n-k$
3. $x[n]*h[n]=\sum_{k'=\infty}^{-\infty}(x[n-k']h[k'])$ from 1 and 2
4. $x[n]*h[n]=h[n]*x[n]$

## Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva