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Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time.
Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstable
Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstable
- a)Both A and R are true and R is a correct explanation of A.
- b)Both A and R are true but R is not a correct explanation of A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'B'. Can you explain this answer?
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Assertion (A): A system is said to be stable if the impulse response a...
Both assertion and reason are individually true. The correct reason for assertion is BIBO stability criteria,
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Assertion (A): A system is said to be stable if the impulse response a...
Answer:
Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time.
Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstable.
Explanation:
To understand the assertion and reason given in the question, let's first define impulse response and stability.
Impulse Response: The impulse response of a system is the output of the system when an impulse input is applied to it. It characterizes the behavior of the system and provides information about how the system responds to sudden changes.
Stability: A system is said to be stable if its output remains bounded for any bounded input. In other words, a stable system does not exhibit unbounded or explosive behavior.
Impulse Response and Stability:
In a stable system, the impulse response approaches zero as time approaches infinity. This means that the system settles down and its output becomes negligible over time. The system is able to handle sudden changes in input without exhibiting unbounded or explosive behavior.
On the other hand, if the impulse response approaches infinity for sufficiently large time, it indicates that the system is unstable. An unstable system does not settle down and its output becomes unbounded or explosive over time. This means that even small changes in the input can lead to significant changes in the output, resulting in an unpredictable behavior.
Validity of Assertion and Reason:
Both Assertion (A) and Reason (R) are true. The impulse response approaching zero for sufficiently large time is a characteristic of a stable system, and the impulse response approaching infinity for sufficiently large time indicates an unstable system. Therefore, both A and R are true.
However, Reason (R) is not a correct explanation of Assertion (A). The reason provided does not explain why the impulse response approaching zero indicates stability or why the impulse response approaching infinity indicates instability. It only states the definitions of stability and instability without providing a direct explanation for Assertion (A).
Hence, the correct answer is option B - Both A and R are true but R is not a correct explanation of A.
Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time.
Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstable.
Explanation:
To understand the assertion and reason given in the question, let's first define impulse response and stability.
Impulse Response: The impulse response of a system is the output of the system when an impulse input is applied to it. It characterizes the behavior of the system and provides information about how the system responds to sudden changes.
Stability: A system is said to be stable if its output remains bounded for any bounded input. In other words, a stable system does not exhibit unbounded or explosive behavior.
Impulse Response and Stability:
In a stable system, the impulse response approaches zero as time approaches infinity. This means that the system settles down and its output becomes negligible over time. The system is able to handle sudden changes in input without exhibiting unbounded or explosive behavior.
On the other hand, if the impulse response approaches infinity for sufficiently large time, it indicates that the system is unstable. An unstable system does not settle down and its output becomes unbounded or explosive over time. This means that even small changes in the input can lead to significant changes in the output, resulting in an unpredictable behavior.
Validity of Assertion and Reason:
Both Assertion (A) and Reason (R) are true. The impulse response approaching zero for sufficiently large time is a characteristic of a stable system, and the impulse response approaching infinity for sufficiently large time indicates an unstable system. Therefore, both A and R are true.
However, Reason (R) is not a correct explanation of Assertion (A). The reason provided does not explain why the impulse response approaching zero indicates stability or why the impulse response approaching infinity indicates instability. It only states the definitions of stability and instability without providing a direct explanation for Assertion (A).
Hence, the correct answer is option B - Both A and R are true but R is not a correct explanation of A.
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Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time.Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstablea)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'B'. Can you explain this answer?
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Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time.Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstablea)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'B'. 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 Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time.Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstablea)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time.Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstablea)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'B'. Can you explain this answer?.
Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time.Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstablea)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'B'. 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 Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time.Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstablea)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time.Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstablea)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'B'. Can you explain this answer?.
Solutions for Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time.Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstablea)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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ample number of questions to practice Assertion (A): A system is said to be stable if the impulse response approaches zero for sufficiently large time.Reason (R): If the impulse response approaches infinity for sufficiently large time, the system is said to be unstablea)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GATE tests.
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