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Consider the following statements for continuous-time linear time invariant (LTI) systems.
I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.
II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.
I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.
II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.
Q. Which one among the following is correct?
- a)Both I and II are true
- b)Both I and II are not true
- c)Only I is true
- d)Only II is true
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Consider the following statements for continuous-time linear time inva...
If a system is non-causal then a pole on right half of the s-plane can give BIBO stable system. But for a causal system to be BIBO all poles must lie on left half of the complex plane.
Most Upvoted Answer
Consider the following statements for continuous-time linear time inva...
Statement I: There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.
Explanation:
- A continuous-time linear time-invariant (LTI) system is BIBO stable if and only if all its poles are in the left half of the complex plane.
- The left half of the complex plane is the region where the real parts of the complex numbers are negative.
- The right half of the complex plane is the region where the real parts of the complex numbers are positive.
- In other words, for a system to be BIBO stable, all its poles must have negative real parts.
Statement II: There is non-causal and BIBO stable system with a pole in the right half of the complex plane.
Explanation:
- A system is causal if the output at any time depends only on the present and past inputs.
- A non-causal system is one where the output at a certain time depends on future inputs, which is not physically realizable.
- BIBO stability is a property that depends only on the system's poles and zeros, and not on causality.
- Therefore, it is possible to have a non-causal system that is BIBO stable with a pole in the right half of the complex plane.
Conclusion:
- Statement I is true because a BIBO stable system cannot have poles in the right half of the complex plane.
- Statement II is true because BIBO stability does not depend on causality, and it is possible to have a non-causal system that is BIBO stable with a pole in the right half of the complex plane.
- Therefore, the correct answer is option D, "Only II is true."
Explanation:
- A continuous-time linear time-invariant (LTI) system is BIBO stable if and only if all its poles are in the left half of the complex plane.
- The left half of the complex plane is the region where the real parts of the complex numbers are negative.
- The right half of the complex plane is the region where the real parts of the complex numbers are positive.
- In other words, for a system to be BIBO stable, all its poles must have negative real parts.
Statement II: There is non-causal and BIBO stable system with a pole in the right half of the complex plane.
Explanation:
- A system is causal if the output at any time depends only on the present and past inputs.
- A non-causal system is one where the output at a certain time depends on future inputs, which is not physically realizable.
- BIBO stability is a property that depends only on the system's poles and zeros, and not on causality.
- Therefore, it is possible to have a non-causal system that is BIBO stable with a pole in the right half of the complex plane.
Conclusion:
- Statement I is true because a BIBO stable system cannot have poles in the right half of the complex plane.
- Statement II is true because BIBO stability does not depend on causality, and it is possible to have a non-causal system that is BIBO stable with a pole in the right half of the complex plane.
- Therefore, the correct answer is option D, "Only II is true."
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Consider the following statements for continuous-time linear time invariant (LTI) systems.I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.Q. Which one among the following is correct?a)Both I and II are trueb)Both I and II are not truec)Only I is trued)Only II is trueCorrect answer is option 'D'. Can you explain this answer?
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Consider the following statements for continuous-time linear time invariant (LTI) systems.I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.Q. Which one among the following is correct?a)Both I and II are trueb)Both I and II are not truec)Only I is trued)Only II is trueCorrect answer is option 'D'. 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 Consider the following statements for continuous-time linear time invariant (LTI) systems.I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.Q. Which one among the following is correct?a)Both I and II are trueb)Both I and II are not truec)Only I is trued)Only II is trueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements for continuous-time linear time invariant (LTI) systems.I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.Q. Which one among the following is correct?a)Both I and II are trueb)Both I and II are not truec)Only I is trued)Only II is trueCorrect answer is option 'D'. Can you explain this answer?.
Consider the following statements for continuous-time linear time invariant (LTI) systems.I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.Q. Which one among the following is correct?a)Both I and II are trueb)Both I and II are not truec)Only I is trued)Only II is trueCorrect answer is option 'D'. 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 Consider the following statements for continuous-time linear time invariant (LTI) systems.I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.Q. Which one among the following is correct?a)Both I and II are trueb)Both I and II are not truec)Only I is trued)Only II is trueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements for continuous-time linear time invariant (LTI) systems.I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.Q. Which one among the following is correct?a)Both I and II are trueb)Both I and II are not truec)Only I is trued)Only II is trueCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Consider the following statements for continuous-time linear time invariant (LTI) systems.I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.Q. Which one among the following is correct?a)Both I and II are trueb)Both I and II are not truec)Only I is trued)Only II is trueCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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Consider the following statements for continuous-time linear time invariant (LTI) systems.I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.Q. Which one among the following is correct?a)Both I and II are trueb)Both I and II are not truec)Only I is trued)Only II is trueCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Consider the following statements for continuous-time linear time invariant (LTI) systems.I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.Q. Which one among the following is correct?a)Both I and II are trueb)Both I and II are not truec)Only I is trued)Only II is trueCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Consider the following statements for continuous-time linear time invariant (LTI) systems.I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.Q. Which one among the following is correct?a)Both I and II are trueb)Both I and II are not truec)Only I is trued)Only II is trueCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider the following statements for continuous-time linear time invariant (LTI) systems.I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.Q. Which one among the following is correct?a)Both I and II are trueb)Both I and II are not truec)Only I is trued)Only II is trueCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice GATE tests.
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