(Solved): Consider the following system for discrete-time filtering of a continuous-time signal: Assume that ...

Consider the following system for discrete-time filtering of a continuous-time signal: Assume that the frequency response of the discrete-time system is \( H\left(e^{j \dot{\omega}}\right)=2 e^{-j 2 \dot{\omega}}-2 e^{-j 7 \dot{\omega}} \). (a) Make a plot of the magnitude response for \( H\left(e^{j \dot{\omega}}\right) \) over the frequency range \( -\pi<\hat{\omega} \leq \pi \). (b) In this part, assume that the input is \[ x(t)=15+20 \cos (800 \pi t+0.1 \pi) \text { for }-\infty