An LTI discrete-time system has frequency response given by (a) Use one of...

An LTI discrete-time system has frequency response given by

(a) Use one of the above forms of the frequency response to obtain an equation for the impulse response h[n] of the system.

(b) From the frequency response, determine the difference equation that is satisfied by the input x[n] and the output y[n] of the system.

(c) If the input to this system is

x[n] = 4 + 2 cos(ω₀n) for−∞< n < ∞,

for what value of ω₀ will the output be of the form

y[n] = A = constant

for −∞ < n < ∞? What is the constant A?