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] $

Back to ECE301 Summer 2008

Alumni Liaison

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

Francisco Blanco-Silva