(Solved): A linear time-invariant system is described by the difference equation \[ y[n]=x[n]+x[n-4] \] (a) F ...

A linear time-invariant system is described by the difference equation \[ y[n]=x[n]+x[n-4] \] (a) Find its impulse response \( h[n] \). (b) Find its system function \( H(z) \). (c) Plot the poles and zeros of \( H(z) \) in the z-plane. (Recall that \( -1=e^{j \pi k} \) where \( k \) is an odd integer.) (d) Find the frequency response \( H\left(e^{j} \Omega\right) \) and express it in polar form (magnitude and phase). (e) Carefullv sketch and label a plot of \( \left|H\left(e^{/ \Omega}\right)\right| \) for \( -\pi<\hat{\omega}<\pi \).