3.18. A causal LTI system has the system function
$H(z) = \frac{1 + 2z^{-1} + z^{-2}}{(1 + \frac{1}{2}z^{-1})(1 - z^{-1})}$
(a) Find the impulse response of the system, $h[n]$.
(b) Find the output of this system, $y[n]$, for the input
$x[n] = e^{j(\pi/2)n}$.