Suppose we are given the following three facts about the signal x(t): 1. x(t) = 0 for t

Chapter 9, Problem 9.12

(choose chapter or problem)

Suppose we are given the following three facts about the signal x(t):

1. \(x(t)=0 \text { for } t<0\).

2. \(x(k / 80)=0\) for \(k=1,2,3, \ldots\)

3. \(x(1 / 160)=e^{-120}\).

Let X(s) denote the Laplace transform of x(t), and determine which of the following statements is consistent with the given information about x(t):

(a) X(s) has only one pole in the finite s-plane.

(b) X(s) has only two poles in the finite s-plane.

(c) X(s) has more than two poles in the finite s-plane.

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