Consider the LTI system whose system function is (a) Determine all causal s...

Consider the LTI system whose system function is

(a) Determine all causal system functions that result in the same frequency-response magnitude as H(z) and for which the impulse responses are real valued and of the same length as the impulse response associated with H(z). (There are four different such system functions.) Identify which system function is minimum phase and which, to within a time shift, is maximum phase.

(b) Determine the impulse responses for the system functions in part (a).

(c) For each of the sequences in part (b), compute and plot the quantity

for 0 ≤ n ≤ 5. Indicate explicitly which plot corresponds to the minimum-phase system.