Consider an LTID system described by the difference equation 4y[n + 2] − y[n] = x[n + 2]+x[n].

a. Plot the pole-zero diagram for this system.

b. Plot the system's magnitude response |H(e^{jΩ})|over-π≤Ω≤π.

c. What type of system is this: low pass, high-pass, band pass, or band stop?

d. Is this system stable? Justify your answer.

e. Is this system real? Justify your answer.

f. If the system input is of the form x[n]=cos (Ω^{n}), what is the greatest possible amplitude of the output? Justify your answer.

g. Draw an efficient, causal implementation of this system using only add, scale, and delay blocks.