Consider the following $AP(3)$ model: $x(n)=0\mathrm{.}98x(n-3)+w(n),$ where $w(n)$

$WGN(0,1).$

$($a$)$ Plot the PSD of $x(n)$ and check if the obtained process is going to exhibit a pseudo$-$

periodic behavior.

$($b$)$ Generate and plot $100$ samples of the process. Does the graph support the conclusion

of part $($a$)?$ If yes, what is the period?

$($c$)$ Compute and plot the PSD of the process $y(n)=\frac{1}{3}[x(n-1)+x(n)+x(n+1)].$

$($d$)$ Repeat part $($b$)$ and explain the difference between the behavior of processes $x(n)$

and $y(n).$

Use Matlab for everything with explanation please!