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GATE 2020 EE – Question 13

Signals and Systems · Applications of Fourier Transform for continuous and discrete time signals, Laplace Transform and Z transform · 1 mark · Multiple choice

Which of the following statements is true about the two sided Laplace transform?

  1. It exists for every signal that may or may not have a Fourier transform.
  2. It has no poles for any bounded signal that is non-zero only inside a finite time interval.
  3. The number of finite poles and finite zeroes must be equal.
  4. If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles.

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Show answer and explanation

Correct answer: (B) It has no poles for any bounded signal that is non-zero only inside a finite time interval.

Explanation

A bounded signal that is non-zero only over a finite time interval has a Laplace transform that is an entire function, so it converges everywhere and has no poles. The Laplace transform does not exist for every signal (A is false), and the numbers of poles and zeros need not be equal (C is false). A weighted sum of one-sided exponentials has poles at the exponent rates (D is false).