$2.$ x$1[$n$]=2$$[$$]+$ $[$ $2]+4$$[$ $3]+6$$[$ $1],$ and $]-$

Draw the following symbols for the signs. The N$-$point AFD of the signs x$[$n$],$ x$2[$n$]$ is given below as X$1,$k and X$2,$k$.$

$($a$)$ directly

$($b$)$ Calculate in terms of X$1,$k and X$2,$k$.($Choose N appropriately.$)$

i$)($x$1[$n$5])4$

ii$)($x$2[2-$n$])4$

iii$)$ y$1[$n$]=($x$1[$n$-2])4*12[$n$]($LINEAR CONVOLUTION$)$

iv$)$ y$2[$n$]=$ x$1[$n$]($x$2[$n$-2])4(4-$POINT CIRCULAR CONVOLUTION$)$