(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'...) |
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==Communative Property for Discrete Time== | ==Communative Property for Discrete Time== | ||
Given: | Given: | ||
| + | |||
<math>y[n]=x[n]*h[n]=\sum_{k=-\infty}^{\infty}(x[k]h[n-k])</math> | <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> |
Revision as of 12:15, 16 November 2008
Communative Property for Discrete Time
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] $
