2. The z-transform of x(n) = au(n) (where u(n) is the unit-step) is X(z) = z/(z-a)...

  

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2. The z-transform of x(n) = a¹u(n) (where u(n) is the unit-step) is X(z) = z/(z-a) with an ROC given by |z| > |a|. (a) Find the z-transform and ROC of (-1) x(n). (b) Find the z-transform and ROC of n x(n). (c) Find the inverse z-transform of X(1/z). (d) Using the Laurent series expansion of X(z) about z = a, prove that z = a is a pole and not an essential singularity. 2. The z-transform of x(n) = a¹u(n) (where u(n) is the unit-step) is X(z) = z/(z-a) with an ROC given by |z| > |a|. (a) Find the z-transform and ROC of (-1) x(n). (b) Find the z-transform and ROC of n x(n). (c) Find the inverse z-transform of X(1/z). (d) Using the Laurent series expansion of X(z) about z = a, prove that z = a is a pole and not an essential singularity.

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