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}u[n]. \ $

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

$ x[n]= u[n] \ $

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Answer 1

$ y[n]=h[n]*x[n]=\sum_{k=-\infty}^\infty \frac{1}{5^k}u[k]u[n-k]=\sum_{k=0}^\infty \frac{1}{5^k}u[n-k]=\Bigg( \sum_{k=0}^n \frac{1}{5^k} \Bigg)u[n] $

I'm not totally sure that this is the way to compute this sum...

$ y[n]=\Bigg(\frac{1-(1/5)^{n+1}}{1-(1/5)}\Bigg)u[n] $

--Cmcmican 20:57, 31 January 2011 (UTC)

The sum appears to be computed correctly. (Clarkjv 23:46, 31 January 2011 (UTC))

Answer 2

Write it here.

Answer 3

Write it here.

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