Solve the difference equation using the z-transform x(n XXXXXXXXXXx(n XXXXXXXXXXx(n) = 0 with initial condition x(0) = 0 and x(1) = 1/2. The signal x(n) is causal For the z-transform H(z) = identify...

Solve the difference equation using the z-transform x(n + 2) - x(n + 1) + x(n) = 0 with initial condition x(0) = 0 and x(1) = 1/2. The signal x(n) is causal For the z-transform H(z) = identify possible regions of convergence and find the inverse z-transform for each of them. For each case comment stability and causality. What is the output of the stable system to x(n) = 1 + (-1) n ?