# 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] \$

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

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))