$5.(20\%)$ Consider the following signals:

x$($n$)=\{1,3,5,3\}$ and y$($n$)=\{1,2,3,4\}$

$*$ Note: First element in each set corresponds to n $=0,$ and the last element corresponds to n $=3.$

$($a$)$ Compute the $4-$point circular convolution z$($n$)=$ x$($n$)$ y$($n$)$ for $0$ n $3.$

$($b$)$ Compute the four$-$point DFT X$($k$)$ and Y $($k$)$ for the signals x$($n$)$ and y$($n$)$ for $0$ k $3.$

$($c$)$ Compute the DFT Z$($k$)$ of the signal z$($n$)$ using X$($k$)$ and Y $($k$)$ obtained in part $($b$).$

$($d$)$ Compute the IDFT $($inverse DFT$)$ of Z$($k$)$ in part $($c$).$