Consider an even sequence x[n] (i.e., x[n] = x[ -n]) with rational z-transform X(z). (a)
Chapter 10, Problem 10.43(choose chapter or problem)
Consider an even sequence x[n] (i.e., x[n] = x[ -n]) with rational z-transform X(z). (a) From the definition of the z-transform, show that X(z) = x(H (b) From your results in part (a), show that if a pole (zero) of X(z) occurs at z = zo, then a pole (zero) must also occur at z = 1/z0 . (c) Verify the result in part (b) for each of the following sequences: (1) o[n + 1] + o[n - 1] (2) o[n + 1] - ~o[n] + o[n- 1]
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