Consider an LTI system whose response to the input

is output y$($t$)$

x$($t$)=[$e$-$t $+$e$-3$t$]$u$($t$)$ y$($t$)=[2$e$-$t $-2$e$-4$t$]$u$($t$)$

EE$603$ Final

$.$

$($a$)$ Find the frequency response of this system.

$($b$)$ What is the system response h$($t$)?$

$($c$)$ Find the differential equation relating the input and output of this system.