(Solved): Please solve step by step A linear time-invariant system is described by the difference equation ...

Please solve step by step

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 $$?1=e^{j?k}$$ where $$k$$ is an $$odd$$ integer.) (d) Find the frequency response $$H\left(e^j?\right)$$ and express it in polar form (magnitude and phase). (e) Carefullv sketch and label a plot of $$\left|H\left(e^{j?}\right)\right|$$ for $$??<\widehat{?}<?$$.