A causal LTI system is described by the difference equation (a) Determine t...

A causal LTI system is described by the difference equation

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

(b) Determine the impulse response of the system.

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