(a) Let h[n] be the impulse response of a real, causal, discrete-time LTI system. Show t...

(a) Let h[n] be the impulse response of a real, causal, discrete-time LTI system. Show that the system is completely specified by the real part of its frequency response. (Hint: Show how h[n] can be recovered from . What is the Fourier transform of This is the discrete-time counterpart of the real part sufficiency property of causal LTI systems considered in Problem 4.47 for continuous-time systems.

(b) Let h[n] be real and causal. If

determine

(c) Show that h[n] can be completely recovered from knowledge of and h[0].

(d) Find two real, causal LTI systems whose frequency responses have imaginary parts equal to sin co.