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