1. A causal discrete-time system is described by a linear constant- coefficient difference equation y[n+2]=y[n+1]−0.5y|n]+x[n+1] (a) Obtain the z-tranform of the unit impulse response h[n]. Pro- vide the ROC and the

poles and zeros. Is the system BIBO stable? Does the Fourier transform converge in the ROC? (b) Given the initial conditions y [0] = 0 and y[1] = 1, provide the ROC of Y (2) and obtain the output signal y[n] for a unit step input x [n] = u[n] using the partial fraction method for the inverse z- transform. Express y [n] as a real-valued solution using the polar form of a complex number reje = rcos 0 + jrsin 0. Give the steady-state solution of y [n] as n → ∞⁰.