Question $2(8$pts$)$: Given a $4-$point signal $[]$: $[0]=3,[1]=2,[2]=$

$1,$ and $[3]=4.$ Let $[]=1[]+2[],$ where $1[]=0$ for odd $,$

and $2[]=0$ for even $.$ Both $1[]$ and $2[]$ are $4-$point signals.

$($a$)$ Find the $4-$point DFT of $1[].$

$($b$)$ Find the $4-$point DFT of $2[].$

$($c$)$ Find the $4-$point DFT of $[].$