Consider the system in Figure P2.76, where the subsystems S1 and S2 are LTI. (a...

Consider the system in Figure P2.76, where the subsystems S₁ and S₂ are LTI.

(a) Is the overall system enclosed by the dashed box, with input x[n] and output y[n] equal to the product of y₁[n] and y₂[n], guaranteed to be an LTI system? If so, explain your reasoning. If not, provide a counterexample.

(b) Suppose S₁ and S₂ have frequency responses H₁(e^jω) and H2(e^jω) that are known to be zero over certain regions. Let

Suppose also that the input x[n] is known to be bandlimited to 0.3π, i.e.,

Over what region of guaranteed to be zero?