Problem 5 An LTI system has unit impulse response h[n] = u[n] -u[n-2].
a.) Compute the system's function
$ H(z) = \sum^{\infty}_{k=-\infty} (u[k]-u[k-2])z^{-k} $
$ = 1 + 1/z \,\ $
b.) Use your answer in a) to compute the system's response to the input x[n] = cos(pi n)
$ cos(pi n) = (-1)^n \,\ $
and we plug that in into the previous equation and get it to be 0.
