Consider the system in Figure, 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 ever certain regions. Let 

Suppose also that the input x[n] is known to be band limited to 0.3π, i.e., Over what region of – π ≤ ω < π is Y(e^jω), the DTFT of y[n], guaranteed to be zero?

Transcribed Image Text:

yı[n] S1 y[n] x[n] S2 y2[n] Part b 0, unspecified, 0.27 < |w\ < x, |wl < 0.27, Hi(ei") = Sunspecified, lw| < 0.47, 0, H2(ei") = 0.47 < lwl < 7. unspecified, Jwl < 0.37, 0, X (ej®) = 0.37 < lw| < .