A causal LTI system is described by the difference equation
y[n] = y[n — 1] + y[n — 2] + x[n – 1]
(a) Find the system function H(z) = Y(z)/ X(z) for this system. Plot the poles and zeros of 11(z) and indicate the region of convergence.
(b) Find the unit sample response of the system.
(c) You should have found the system to be unstable. Find a stable (noncausal) unit sample response that satisfies the difference equation.
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