(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...)
 
(Problem 5)
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<math>u[k]={ 1, k > 0
 
<math>u[k]={ 1, k > 0
             0, else     
+
             0, else}      
 
</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) $.

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Recent Math PhD now doing a post-doctorate at UC Riverside.

Kuei-Nuan Lin