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

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

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