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 zeroes of H(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 ( but non- causal ) unit sample response which satisfies the difference equation.