$14.$ Let x$1[$n$]=1$

$,2,3,4,5$ be a $5-$point sequence and let x$2[$n$]=2$

$$

$,1,1,1$ be a

$4-$point sequence.

$($a$)$ Determine x$1[$n$]$ m $5$ x$2[$n$]$using hand calculations.

$($b$)$ Verify your calculations in $($a$)$ using the circonv function.

$($c$)$ Verify your calculations in $($a$)$ by computing the DFTs and IDFT.