Line 1: Line 1:
 
== Question 3. ==
 
== Question 3. ==
 
* An LTI system has unit impulse response h[n] =u[-n]. Compute the system's response to the input <math>x[n] = 2^{n}u[-n].</math> Simplify your answer until all <math> \sum</math> signs disappear.)
 
* An LTI system has unit impulse response h[n] =u[-n]. Compute the system's response to the input <math>x[n] = 2^{n}u[-n].</math> Simplify your answer until all <math> \sum</math> signs disappear.)
 +
 +
 +
== Answer ==
 +
<math> y[n] = x[n] * h[n] , where * is convolution,\</math>
 +
 +
<math> \sum^{\infty}_{k=-\infty} 2^{k}u[-k]u[-n+k]</math>

Revision as of 13:22, 10 October 2008

Question 3.

  • An LTI system has unit impulse response h[n] =u[-n]. Compute the system's response to the input $ x[n] = 2^{n}u[-n]. $ Simplify your answer until all $ \sum $ signs disappear.)


Answer

$ y[n] = x[n] * h[n] , where * is convolution,\ $

$ \sum^{\infty}_{k=-\infty} 2^{k}u[-k]u[-n+k] $

Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett