2 (20', bonus) (Inverse z-transform) Consider the discrete-time system described by H(z) = 1 (1 z1)(1 1 2z1) . a) Find the impulse response h[n] under the following conditions and comment on whether it is a stable and/or causal system for each of the following cases: (i) If the ROC is |z| > 1. (ii) If the ROC is |z| < 1 2 . (iii) If the ROC is 1 > |z| > 1 2 . b) Sketch the magnitude of the frequency response of this system |H(ej)| using the pole- zero plot. Note that this is unaffected by the ROC