Consider the FIR system defined by the difference equation

$y[n]=x[n-1]-x[n-2]+x[n-3]$

$($a$)$ determine the impulse response of the system

$($b$)$ implement the system in Simulink in direct form $($tapped$-$delay$)$

$($c$)$ via simulink, determine the response of the system you implemented in $4b$ to the input $x[n]=\{3,2,-2,8\}.$

$($d$)$ use the convolution sum to determine the response of the system to $x[n]=\{3,2,-2,8\}.$