Problem $8\mathrm{.}1$ Video Problem, $10$ points

Explain your solution step$-$by$-$step like you were trying to teach one of your classmates how to solve this problem.

This problem examines processing a continuous$-$time signal in discrete time using the system shown below

The discrete$-$time filter has the frequency response $H_d(e^j)$ shown below

Assume that $x_c(j),$ the Fourier transform for the input signal, is

Sketch the Fourier transforms $x_d(e^j),Y_d(e^j)$ and $Y_c(j).$ You must label all important frequencies and amplitudes to receive full credit.