Question

$y\left(t\right)$ is the response of an LTI system whose x(t) and h(t) are shown then the value of y(0)+y(1) is ____

• A. 8

Answer 1

The correct option is A 8

$y\left(t\right)={\int }_{-\infty }^{\infty }x\left(\tau \right)h(t-\tau )d\tau$

For $t<-2,y\left(t\right)=0$

For $-2\le t<0y\left(t\right)={\int }_{-\infty }^{t+2}2d\tau =2t+4$

For $0\le t<1y\left(t\right)={\int }_0^{2}2d\tau =2\tau {|}_0^2=4$

For $1\le t<3y\left(t\right)={\int }_{t-1}^{2}2d\tau =6-2t$

For $t>3y\left(t\right)=0$

$\therefore y\left(0\right)=4$

$y\left(1\right)=4$

$y\left(0\right)+y\left(1\right)=4+4=8$