## Contents

# Practice Question on Computing the Output of an LTI system by Convolution

The unit impulse response h[n] of a DT LTI system is

$ h[n]= \frac{1}{3^n} \ $

Use convolution to compute the system's response to the input

$ x[n]= \delta[n+2]+\delta[n+1]+\delta[n]+\delta[n-1]. \ $

You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!

### Answer 1

$ y[n]=h[n]*x[n]=\sum_{k=-\infty}^\infty \frac{1}{3^k}\delta[n+2-k]+\sum_{k=-\infty}^\infty \frac{1}{3^k}\delta[n+1-k]+\sum_{k=-\infty}^\infty \frac{1}{3^k}\delta[n-k]+\sum_{k=-\infty}^\infty \frac{1}{3^k}\delta[n-1-k] $

$ y[n]=\frac{1}{3^{n+2}}+\frac{1}{3^{n+1}}+\frac{1}{3^{n}}+\frac{1}{3^{n-1}} $

--Cmcmican 20:25, 31 January 2011 (UTC)

### Answer 2

Write it here.

### Answer 3

Write it here.