## Answers

X_a (n) = delta (n) x_a (z) = 1 ROC: entire z plane x_b (n) = r^n cos w_0 n 4_1 (n) cos w_0 n u (n) rightarrow z (z - cos w_0)/z^2 - 2 z cos w_0 + 1 ROC: Vertical-bar z Vertical-bar > 1 By time mortifications property r^n cos w_0 n mu (n) z. t z (z - cos w_0)/z^2 - 2 z cos w_0 + 1 z rightarrow z/r ROC: z/r Vertical-bar > Vertical-bar z/r (z/r - cos w_0) (z/r)^2 - 2 z/r cos w_0 + 1 (z - r cos w_0)/z^2 - 2 z y cos w_0 + r^2: (z) > r x_b (z) = z (z + r cos w_0)/z^2 - 2 z r cos w_0 + r^2 RoC: Vertical-bar z Vertical-bar > r x_c (n) = r^2 sin w_0 n 4 (n) sin w_0 n u (n) z. T z sin w_0/z^2 - 2 z cos w_0 + 1 ROC: Vertical-bar z Vertical-bar > 1 r^2 sin w_0 n u (n) z

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