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(ejΩ)|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 (Ωn), 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.