Consider the linear time-invariant system whose system function is

?H(z) = (1 ? 0.9e^j0.6??z^?1)(1 ? 0.9e^?j0.6? z^?1)(1 ? 1.25e^j0.8??z^?1)(1 ? 1.25e^?j0.8? z^?1).

(a) Find all causal system function 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 function) Identify which system function is minimum phase and which, to within a time shift, is maximum phase.

(b) Find 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.

E(n] = (h[m])