Question $1$:

$($a$)$ The response of a lincar time$-$invariant $($LTI$)$ system to an input $x_1(t)=u(t)-u(t-1)$ is a function $y_1(t).$ What is the response $y_2(t)$ of the system, in terms of $y_1(t),$ if the input is $x_2(t)$ displayed below?

$(10$ marks$)$

$($b$)$ Now, consider another LTI system. The input $x_1^{\text{'}}(t)=2u(t-1)-u(t-2)-u(t-3)$ generates a response $y_1^{\text{'}}(t).$ Find the response $y_2^{\text{'}}(t)$ of this system, in terms of $y_1^{\text{'}}(t),$ if the input is $x_2^{\text{'}}(t)=x_2(t).$

$(10$ marks$)$

Note: Use only time domain analysis.