Consider the system in Figure P 2.76, where the subsystems S ₁ and S ₂ 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 y ₁ [n] and y ₂ [n], guaranteed to be an LTI system? If so, explain your reasoning. If not, provide a counterexample.

(b) Suppose S ₁ and S ₂ , have frequency responses H ₁ (e ^j? ) and H ₂ (e ^j? ) that are known to be zero over certain regions. Let

Suppose also that the input x[n] is known to be band limited to 0.3?, i.e

Over what region of -? ? ? j? ), the DTFT of y[n], guaranteed to be zero?

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a Refer to Figure P276 in the text book The sub systems S 1 and S 2 are linear The relation between ... View the full answer