(New page: ==Communative Property for Discrete Time== Given: <math>y[n]=x[n]*h[n]=\sum_{k=-\infty}^{\infty}(x[k]h[n-k])</math> #<math>x[n]*h[n]=\sum_{k=-\infty}^{\infty}(x[k]h[n-k])</math> #<math>k'...) |
|||
| (6 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| − | = | + | [[Category: ECE]] |
| − | Given: | + | [[Category: ECE 301]] |
| − | <math>y[n]=x[n]*h[n]=\sum_{k=-\infty}^{\infty}(x[k]h[n-k])</math> | + | [[Category: Summer]] |
| + | [[Category: 2008]] | ||
| + | [[Category: asan]] | ||
| + | [[Category: Bonus]] | ||
| + | =Proof of the Commutativity property of LTI systems ([[ECE301]])= | ||
| + | Given: <math>y[n]=x[n]*h[n]=\sum_{k=-\infty}^{\infty}(x[k]h[n-k])</math> | ||
| − | #<math>x[n]*h[n]=\sum_{k=-\infty}^{\infty}(x[k]h[n-k])</math> | + | #<math> x[n]*h[n]=\sum_{k=-\infty}^{\infty}(x[k]h[n-k])</math> |
| − | #<math>k'=n-k</math> | + | #<math> k'=n-k</math> |
| − | #<math>x[n]*h[n]=\sum_{k'=\infty}^{-\infty}(x[n-k']h[k'])</math> from 1 and 2 | + | #<math> x[n]*h[n]=\sum_{k'=\infty}^{-\infty}(x[n-k']h[k'])</math> from 1 and 2 |
| − | #<math>x[n]*h[n]=h[n]*x[n]</math> | + | #<math> x[n]*h[n]=h[n]*x[n]</math> |
| + | ---- | ||
| + | [[ECE_301_%28SanSummer2008%29|Back to ECE301 Summer 2008]] | ||
Latest revision as of 10:27, 30 January 2011
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] $
