An LTI system has the frequency response (a) Specify the difference equatio...

An LTI system has the frequency response

(a) Specify the difference equation that is satisfied by the input x[n] and the output y[n].

(b) Use one of the above forms of the frequency response to determine the impulse response h[n].

(c) Show that |H(e^jω)|² = G², where G is a constant. Determine the constant G. (This is an example of an allpass filter to be discussed in detail in Chapter 5.)

(d) If the input to the above system is x[n] = cos(0.2πn), the output should be of the form y[n] = Acos(0.2πn + θ).What are A and θ?