(a) Suppose that x(n) is a finite-duration sequence of N = 1024 points. It is desired to evaluate the z-transform X(z) of the sequence at the points

zk = ej(2π/1024)k k = 0, 100, 200, . . . , 1000

by using the most efficient method or algorithm possible. Describe an algorithm for performing this computation efficiently. Explain how you arrived at your answer by giving the various options or algorithm that can be used.

(b) Repeat part (a) if X(z) is to be evaluated at zk = 2(0.9)kej[(2π/5000)k + π/2] k = 0, 1, 2, . . . , 999