Let x[n] denote a causal sequence (i.e., if x[n] = 0, n < 0) for which x[O] is nonzero
Chapter 10, Problem 10.55(choose chapter or problem)
Let x[n] denote a causal sequence (i.e., if x[n] = 0, n < 0) for which x[O] is nonzero and finite. (a) Using the initial-value theorem, show that there are no poles or zeros of X(z) at z = oo. (b) Show that, as a consequence of your result in part (a), the number of poles of X(z) in the finite z-plane equals the number of zeros of X(z) in the finite z-plane. (The finite z-plane excludes z = oo.)
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