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QUESTION
(a) Define z-transform of sequence x[n].
(b) A causal LTI system has impulse response h[n], for which the z-transform is
H(z) = (1+z-1)/(1-1/2z-1)(1+1/4z-1)
(i) What is the Region of Convergence of H(z)? Plot the poles and zeros in the z-plane.
(ii) Find the impulse response h[n] of the system.
(c) A causal LTI system has impulse response h[n] by:
h[n] = [(0.3)n+(-0.5)n] u[n]
(i) Find the z-transform of h[n].
(ii) Plot the poles and zeros in the z-plane and the shade the Region of convergence.
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