(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). <math>H(z)=\sum_{k=-\infty}^{\infty}h[k]z^{-k}</math> <math>H(z)=\s...) |
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<math>u[k]={ 1, k > 0 | <math>u[k]={ 1, k > 0 | ||
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</math> | </math> | ||
Revision as of 14:39, 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} $
$ H(z)=\sum_{k=-\infty}^{\infty}(u[k]-u[k-2])z^{-k} $
$ u[k]={ 1, k > 0 0, else} $
$ H(z)=\sum_{k=0}^{1}z^{-k} $
b) the system's response to the input $ x[n]=\cos(\pi n) $.
