Consider the discrete-time LTI system with the output signal defined as
\begin{equation}
y[n] = x[n] + \frac{1}{\alpha^2}x[n - 2]
\end{equation}
where $x[n]$ is the signal at the system input and $\alpha$ is a real positive constant value. Let $h[n]$ be the unit impulse
response of the LTI system. Let $g[n]$ be the unit impulse response of the inverse system of $h[n]$. (Recall that
$h[n] * g[n] = \delta[n]$, where $\delta[n]$ is the unit impulse.) Note that both $h[n]$ and $g[n]$ are causal.
A) Compute $h[n]$
B) Compute the z-transform of $h[n]$, i.e., $H(z)$
C) Compute the z-transform of $g[n]$, i.e., $G(z)$
D) Compute $g[n]$
