In Figure P3.42, H(z) is the system function of a causal LTI system. (a) Using z-tr...

In Figure P3.42, H(z) is the system function of a causal LTI system.

(a) Using z-transforms of the signals shown in the figure, obtain an expression for W(z) in the form

where both H₁(z) and H2(z) are expressed in terms of H(z).

(b) For the special case H(z) = z ⁻¹/(1 − z ⁻¹), determine H₁(z) and H₂(z).

(c) Is the system H(z) stable? Are the systems H₁(z) and H₂(z) stable?