Question
Which of the following statements is true about the two sided Laplace transform?
Options :
It exists for every signal that may or may not have a Fourier Transform.
It has no poles for any bounded signal that is non-zero only inside a finite time interval.
If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace
transform will have no poles.
The number of finite poles and finite zeroes must be equal.
Answer :
It has no poles for any bounded signal that is non-zero only inside a finite time interval.
Solution :
From the properties of ROC of Laplace transform :
1. ROC does not contain any pole
2. ROC of transform of a bounded finite duration signal is entire S-plane
It can be said that, if a signal is bounded and exists only for finite duration, then ROC is entire s-plane, so
it can not have any pole as ROC does not contain any pole.
Hence, the correct option is (B)
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