Consider a discrete-time LTI system with frequency response H(ejω) 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(ejω) = 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].
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