The following are three proposed identities involving compressors and expanders. For eac...

The following are three proposed identities involving compressors and expanders. For each, state whether or not the proposed identity is valid. If your answer is that it is valid, explicitly show why. If your answer is no, explicitly give a simple counterexample.

(a) Proposed identity (a):

(b) Proposed identity (b):

(c) Proposed identity (c):

where L is a positive integer, and A is defined in terms of X(e^jω) and Y(e^jω) (the respective DTFTs of A’s input and output) as: