# 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]= \delta[n-1]. \$

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

$x[n]= \frac{1}{2^n} \$

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

$\delta[n-1-k] = \begin{cases} 1, & \mbox{if }k = n-1 \\ 0, & \mbox{if }k \ne n-1 \end{cases}$

$y[n] = \frac{1}{2^{n-1}}$ --Cmcmican 20:13, 31 January 2011 (UTC)