sorul A continous$-$time signal $x(t)$ is shown. Sketch each of the following signal.

a$)x(t-2)$

C$)x(2t+1)$

e$)[x(t)+x(-t)]u(t)$

b$)x(2-+)$

d$)$

Sorve $[n]=2[n+1]+2[n-1]+2[n-1]$ and $h[n]=[n]-[n-3]$ compute and plot eoch of the following convolutions:

a$)y_1[n]=x[n]**h[n]$

b$)y_2[n]=x[n+2]h[n]$

C$)y_3[n]=x[n]**h[n+2]$

Son $3$ consider an input $x[n]$ and a unit impulse fesponse h$[$n$]$ given by

$x[n]=(\frac{1}{s}{)}^{n}u[n]$

$h[n]=u[n]$

Determine and plat the output $y[n]=x[n]**k[n]$

Sorul $x(t)=u(t+3)-u(t-5)$ and $h(t)=e^{-3t}u(t)$

$x(t)longrightarrowh(t)longrightarrowy(t)=$

Sorus consider an LTI system whose input $x(t)$ and output $y(t)$ ore related by $,\frac{dy(t)}{dt}+2y(t)=x(t)$

The system also sotisfies the conalition of initial rest. If $x(t)=e^{-t}U(t),$ what is $y(t)=?$