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

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

W(z) = H₁(z) X(z) + H₂(z) E(z),

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?

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