Question: A causal linear time-invariant system is described by the difference equation y[n] = 3/2 y[n 1] + y[n 2] + [n 1].

A causal linear time-invariant system is described by the difference equation 

 y[n] = 3/2 y[n – 1] + y[n – 2] + [n – 1].

(a) Find the system function H(z) = Y(z) / X(z) for this system. Plot the poles and zeros of H(z), and indicate the region of convergence.

(b) Find the impulse response of the system.

(c) You should have found the system to be unstable. Find a stable (noncausal) impulse response that satisfies the difference equation.

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