It can be shown (see Problem 3.50) that if x[n] = 0 for n < 0, then This re...

It can be shown (see Problem 3.50) that if x[n] = 0 for n < 0, then

This result was called the initial value theorem for right-sided sequences.

(a) Prove a similar result for left-sided sequences, i.e., for sequences such that x[n] = 0 for n > 0.

(b) Use the initial value theorems to prove that if x[n] is a minimum-phase sequence.

(c) Use the initial value theorems to prove that if x[n] is a maximum-phase sequence.

(d) Use the initial value theorems to prove that when X(z) is given by Eq. (13.32). Is this result consistent with the results of parts (b) and (c)?