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}{5^n} . \ $

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

$ x[n]= \delta[n-3]. \ $

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Answer 1

$ y[n]=h[n]*x[n]=\sum_{k=-\infty}^\infty \frac{1}{5^k}\delta[n-3-k]] $

$ y[n]=\frac{1}{5^{n-3}} $

--Cmcmican 20:27, 31 January 2011 (UTC)

Answer 2

Write it here.

Answer 3

Write it here.

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