$($CTFT and Properties for LTI Systems$)(20$ pts$)$ Consider an LTI system whose

response to the input x$($t$)=($e$$t $+$ e$3$t$)$u$($t$)$ is y$($t$)=(2$e$$t $2$e$4$t$)$u$($t$).$

$($a$)$ Find the frequency response H$($j$)$ of the system $($which is similar to transfer function

H$($s$)$ defined in the s$-$domain instead$).$

$($b$)$ Find the system$$s impulse response h$($t$).($Hint: You can rewrite H$($j$)$ as sum of simpler

fractions using partial fraction expansion before applying the inverse Fourier transform.$)$