Q$2$: $[25$ Marks$]$ Consider the following:

y$1$

$($t$)=[\{$cos$($w$0$t$)\}$x$($t$)]$ h$($t$)$ and y$2$

$($t$)=[\{$sin$($w$0$t$)\}$x$($t$)\}]$ h$($t$)$

Where x$($t$)=$ ak

k$=$ e

jk$100$t is real valued periodic signal and h$($t$)$ is the impulse response of a

stable LTI system.

$($a$)$ Find the value of w$0$ and any necessary restrictions on H$($jw$)$ to ensure that

y$1$

$($t$)=$ Re$\{$a$6\}$ and y$2$

$($t$)=$ Img$\{$a$6\}$

$($b$)$ Find h$($t$)$ such that H$($jw$)$ satisfies the restrictions specified in Part $($a$).$