$($Convolution DT$)$ Consider the following LTI system with input $x[n]$ and output $y[n]$ :

$($a$)(5$ pts$)$ Sketch the input signal $x[n]=u[n+2]-u[n].$

$($b$)(5$ pts$)$ Sketch the impulse response signal $h[n]=u[n-1]-u[n-3].$

$($c$)(5$ pts$)$ What is $x[n]**[n]?$ What is $x[n]**[n-k]?($Note $*$ represents convolution.$)$

$($d$)(10$ pts$)$ Use convolution to compute the output signal y$[n$ and sketch the result.