Consider an LTI system with transfer function $H()=2$rect$(\frac{}{4}).$ The input to the system is $x(t)=3sinc(t)+cos(5t).$

$($a$)$ Find the Fourier transform of $x(t).$

$($b$)$ Manually sketch $x()$ and $H().$

$($c$)$ Find $Y()$ at the output of the LTI system.