Assuming ideal D/C amd C/D converters, the overall system of Figure P5.56 is a discrete...

Assuming ideal D/C amd C/D converters, the overall system of Figure P5.56 is a discrete time LTI system with frequency response H(e^jω) and impulse response h[n].

(a) H(e^jω) can be expressed in the form

with A(e^jω) real. Determine and sketch A(e^jω) and φ(ω) for |ω| < π.

(b) Sketch h[n] for the following:

(i) α = 3

(ii) α =

(iii) α =

c) Consider a discrete-time LTI system for which

with A(e^jω) real. What can be said about the symmetry of h[n] for the following?

(i) α = integer

(ii) α = M/2, where M is an odd integer

(iii) General α.