Problem 5
An LTI system has unit impulse response h[n]=u[n]-u[n-2].
a)Compute the system's function H(z).
$ H(z) = \sum_{k=-\infty}^{\infty}h[k]z^{-k}\, $
$ = \sum_{k=-\infty}^{\infty}(u[k]-u[k-2])z^{-k}\, $
$ = \sum_{k=0}^{1}z^{-k}\, $
$ = 1 + \frac{1}{z} $
