(New page: Category: ECE Category: ECE 301 Category: Summer Category: 2008 Category: asan Category: Bonus Given: <math>y[n]=x[n]*h[n]=\sum_{k=-\infty}^{\infty}(x[k]h[n-k])</ma...) |
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Latest revision as of 10:44, 21 November 2008
Given: $ y[n]=x[n]*h[n]=\sum_{k=-\infty}^{\infty}(x[k]h[n-k]) $
- $ x[n]*(h_1[n]*h_2[n])=x[n]*(h_1[n]*h_2[n]) $
- $ x[n]*(h_1[n]*h_2[n])=x[n]*(h_2[n]*h_1[n]) $ Commutative property of discrete time
- $ x[n]*(h_1[n]*h_2[n])=x[n]*(\sum_{k=-\infty}^{\infty}h_2[k]h_1[n-k]) $
- $ x[n]*(h_1[n]*h_2[n])=\sum_{j=-\infty}^{\infty}x[j](\sum_{k=-\infty}^{\infty}h_2[k]h_1[n-k-j]) $
- $ x[n]*(h_1[n]*h_2[n])=\sum_{j=-\infty}^{\infty}\sum_{k=-\infty}^{\infty}x[j](h_2[k]h_1[n-k-j]) $
- $ x[n]*(h_1[n]*h_2[n])=\sum_{j=-\infty}^{\infty}\sum_{k=-\infty}^{\infty}h_2[k]x[j]h_1[n-k-j] $
- $ x[n]*(h_1[n]*h_2[n])=\sum_{k=-\infty}^{\infty}h_2[k]\sum_{j=-\infty}^{\infty}x[j]h_1[n-k-j] $
- $ x[n]*(h_1[n]*h_2[n])=h_2[n]*\sum_{j=-\infty}^{\infty}x[j]h_1[n-j] $
- $ x[n]*(h_1[n]*h_2[n])=h_2[n]*(x[n]*h_1[n]) $
- $ x[n]*(h_1[n]*h_2[n])=(x[n]*h_1[n])*h_2[n] $ Commutative property of discrete time