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Which of the following statements is true about the two sided Laplace transform?
- a)It has no poles for any bounded signal that is non-zero only inside a finite time interval.
- b)If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles.
- c)It exists for every signal that may or may not have a Fourier transform.
- d)The number of finite poles and finite zeroes must be equal.
Correct answer is option 'A'. Can you explain this answer?
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Which of the following statements is true about the two sided Laplace ...
Introduction:
The two-sided Laplace transform is a mathematical tool used to analyze signals in the frequency domain. It is an extension of the one-sided Laplace transform, which is used for signals that are non-zero only for positive time. The two-sided Laplace transform allows for signals that are non-zero for both positive and negative time.
Statement:
The true statement about the two-sided Laplace transform is option 'A', which states that it has no poles for any bounded signal that is non-zero only inside a finite time interval.
Explanation:
To understand why option 'A' is true, let's first define what poles are in the context of the Laplace transform.
Poles:
In the Laplace transform, poles are the values of 's' for which the transform becomes infinite. In other words, they are the values of 's' that make the denominator of the Laplace transform equation equal to zero.
Bounded Signal:
A bounded signal is a signal that does not grow infinitely with time. It remains within a certain range or bound.
Finite Time Interval:
A finite time interval refers to a time duration that is limited or finite. It has a definite start and end time.
No Poles for Bounded Signal:
Option 'A' states that the two-sided Laplace transform has no poles for any bounded signal that is non-zero only inside a finite time interval. This means that if a signal is bounded and non-zero only for a finite duration of time, then its Laplace transform will not have any poles.
The reason for this is that a bounded signal, by definition, does not grow infinitely with time. Hence, its Laplace transform will not have any values of 's' for which the transform becomes infinite (i.e., no poles). Additionally, if the signal is non-zero only inside a finite time interval, then it does not have any impact on the behavior of the transform for infinite time values.
Therefore, option 'A' is true, and the two-sided Laplace transform has no poles for any bounded signal that is non-zero only inside a finite time interval.
The two-sided Laplace transform is a mathematical tool used to analyze signals in the frequency domain. It is an extension of the one-sided Laplace transform, which is used for signals that are non-zero only for positive time. The two-sided Laplace transform allows for signals that are non-zero for both positive and negative time.
Statement:
The true statement about the two-sided Laplace transform is option 'A', which states that it has no poles for any bounded signal that is non-zero only inside a finite time interval.
Explanation:
To understand why option 'A' is true, let's first define what poles are in the context of the Laplace transform.
Poles:
In the Laplace transform, poles are the values of 's' for which the transform becomes infinite. In other words, they are the values of 's' that make the denominator of the Laplace transform equation equal to zero.
Bounded Signal:
A bounded signal is a signal that does not grow infinitely with time. It remains within a certain range or bound.
Finite Time Interval:
A finite time interval refers to a time duration that is limited or finite. It has a definite start and end time.
No Poles for Bounded Signal:
Option 'A' states that the two-sided Laplace transform has no poles for any bounded signal that is non-zero only inside a finite time interval. This means that if a signal is bounded and non-zero only for a finite duration of time, then its Laplace transform will not have any poles.
The reason for this is that a bounded signal, by definition, does not grow infinitely with time. Hence, its Laplace transform will not have any values of 's' for which the transform becomes infinite (i.e., no poles). Additionally, if the signal is non-zero only inside a finite time interval, then it does not have any impact on the behavior of the transform for infinite time values.
Therefore, option 'A' is true, and the two-sided Laplace transform has no poles for any bounded signal that is non-zero only inside a finite time interval.
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Which of the following statements is true about the two sided Laplace transform?a)It has no poles for any bounded signal that is non-zero only inside a finite time interval.b)If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles.c)It exists for every signal that may or may not have a Fourier transform.d)The number of finite poles and finite zeroes must be equal.Correct answer is option 'A'. Can you explain this answer?
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Which of the following statements is true about the two sided Laplace transform?a)It has no poles for any bounded signal that is non-zero only inside a finite time interval.b)If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles.c)It exists for every signal that may or may not have a Fourier transform.d)The number of finite poles and finite zeroes must be equal.Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Which of the following statements is true about the two sided Laplace transform?a)It has no poles for any bounded signal that is non-zero only inside a finite time interval.b)If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles.c)It exists for every signal that may or may not have a Fourier transform.d)The number of finite poles and finite zeroes must be equal.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements is true about the two sided Laplace transform?a)It has no poles for any bounded signal that is non-zero only inside a finite time interval.b)If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles.c)It exists for every signal that may or may not have a Fourier transform.d)The number of finite poles and finite zeroes must be equal.Correct answer is option 'A'. Can you explain this answer?.
Which of the following statements is true about the two sided Laplace transform?a)It has no poles for any bounded signal that is non-zero only inside a finite time interval.b)If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles.c)It exists for every signal that may or may not have a Fourier transform.d)The number of finite poles and finite zeroes must be equal.Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Which of the following statements is true about the two sided Laplace transform?a)It has no poles for any bounded signal that is non-zero only inside a finite time interval.b)If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles.c)It exists for every signal that may or may not have a Fourier transform.d)The number of finite poles and finite zeroes must be equal.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements is true about the two sided Laplace transform?a)It has no poles for any bounded signal that is non-zero only inside a finite time interval.b)If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles.c)It exists for every signal that may or may not have a Fourier transform.d)The number of finite poles and finite zeroes must be equal.Correct answer is option 'A'. Can you explain this answer?.
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