(New page: == Problem 5 == An LTI system has unit impulse response h[n]=u[n]-u[n-2]. a)Compute the system's function H(z).) |
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a)Compute the system's function H(z). | a)Compute the system's function H(z). | ||
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| + | <math>H(z) = \sum_{k=-\infty}^{\infty}h[k]z^{-k}\,</math> | ||
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| + | <math> = \sum_{k=-\infty}^{\infty}(u[k]-u[k-2])z^{-k}\,</math> | ||
| + | |||
| + | <math> = \sum_{k=0}^{1}z^{-k}\,</math> | ||
| + | |||
| + | <math> = 1 + \frac{1}{z}</math> | ||
Revision as of 16:27, 15 October 2008
Problem 5
An LTI system has unit impulse response h[n]=u[n]-u[n-2].
a)Compute the system's function H(z).
$ H(z) = \sum_{k=-\infty}^{\infty}h[k]z^{-k}\, $
$ = \sum_{k=-\infty}^{\infty}(u[k]-u[k-2])z^{-k}\, $
$ = \sum_{k=0}^{1}z^{-k}\, $
$ = 1 + \frac{1}{z} $
