Consider a discrete-time LTI system with frequency response H(ejω) and corresponding imp...

Consider a discrete-time LTI system with frequency response H(e^jω) and corresponding impulse response h[n].

(a) We are first given the following three clues about the system:

(i) The system is causal.

(ii) H(e^jω) = H∗(e^−jω).

(iii) The DTFT of the sequence h[n + 1] is real.

Using these three clues, show that the system has an impulse response of finite duration.

(b) In addition to the preceding three clues, we are now given two more clues:

Is there enough information to identify the system uniquely? If so, determine the impulse response h[n]. If not, specify as much as you can about the sequence h[n].