Problem II$.$

Suppose that thwo systems are connected in cascade

The two systems are specified as follows

$S1$:$y1[n]=x1[n]-x1[n-1]$

S$2$: $y_2[n]=x2[n-1]+x2[n-2]$

$($a$)$ Determine the imoulse response of S$1$ and S$2.$

$($b$)$ Determine the frequency response of S$1$ and S$2.$

$($c$)$ Determine the frequency response of the overall system.

$($d$)$ Write one difference equation that defines the overall system in terms of $x[n]$ and $y[n]$ only.