Let x[n] denote a causal sequence; i.e., x[n] = 0, n < 0. Furthermore, assume that x[0] ≠ 0 and that the z-transform is a rational function.
(a) Show that there are no poles or zeros of X(z) at z=∞, i.e., that is nonzero and finite.
(b) Show that the number of poles in the finite z-plane equals the number of zeros in the finite z-plane. (The finite z-plane excludes z=∞.)
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