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Assertion (A): The discrete time system described by y[n] =2x[n] +4x[n-1] is unstable
Reason (R): It has an impulse response with a finite number of non-zero samples
Reason (R): It has an impulse response with a finite number of non-zero samples
- a)Both A and R are true and R is correct explanation of A
- b)Both A and R are true but R is not correct explanation of A
- c)A is true but R is false
- d)A is false but R is true
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Assertion (A): The discrete time system described by y[n] =2x[n] +4x[n...
Explanation: For the system to be stable the value of the transfer function in the discrete time domain must be summable and H[n] calculated is summable hence the system is stable.
Most Upvoted Answer
Assertion (A): The discrete time system described by y[n] =2x[n] +4x[n...
Assertion (A): The discrete time system described by y[n] = 2x[n] - 4x[n-1] is unstable.
Reason (R): It has an impulse response with a finite number of non-zero samples.
Explanation:
To determine the stability of a discrete-time system, we need to analyze its impulse response. The impulse response of a system is the output of the system when an impulse input is applied.
The given system is described by the equation y[n] = 2x[n] - 4x[n-1]. Let's analyze its impulse response.
Impulse Response:
An impulse input is represented by δ[n], where δ[n] = 1 for n = 0 and δ[n] = 0 for n ≠ 0.
When an impulse input is applied to the system, the output can be calculated as follows:
y[n] = 2x[n] - 4x[n-1]
= 2δ[n] - 4δ[n-1]
For n = 0, y[0] = 2δ[0] - 4δ[-1]
But δ[-1] is not defined in discrete-time systems. Therefore, the system is not defined for n = 0, and we cannot determine the value of y[0].
Since the system is not defined for n = 0, it implies that the system does not have a finite number of non-zero samples in its impulse response. Therefore, the Reason (R) is incorrect.
Conclusion:
The Assertion (A) is true as the system is indeed unstable. However, the Reason (R) is false as the system does not have a finite number of non-zero samples in its impulse response. Hence, the correct answer is option D) A is false but R is true.
Reason (R): It has an impulse response with a finite number of non-zero samples.
Explanation:
To determine the stability of a discrete-time system, we need to analyze its impulse response. The impulse response of a system is the output of the system when an impulse input is applied.
The given system is described by the equation y[n] = 2x[n] - 4x[n-1]. Let's analyze its impulse response.
Impulse Response:
An impulse input is represented by δ[n], where δ[n] = 1 for n = 0 and δ[n] = 0 for n ≠ 0.
When an impulse input is applied to the system, the output can be calculated as follows:
y[n] = 2x[n] - 4x[n-1]
= 2δ[n] - 4δ[n-1]
For n = 0, y[0] = 2δ[0] - 4δ[-1]
But δ[-1] is not defined in discrete-time systems. Therefore, the system is not defined for n = 0, and we cannot determine the value of y[0].
Since the system is not defined for n = 0, it implies that the system does not have a finite number of non-zero samples in its impulse response. Therefore, the Reason (R) is incorrect.
Conclusion:
The Assertion (A) is true as the system is indeed unstable. However, the Reason (R) is false as the system does not have a finite number of non-zero samples in its impulse response. Hence, the correct answer is option D) A is false but R is true.
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Assertion (A): The discrete time system described by y[n] =2x[n] +4x[n-1] is unstableReason (R): It has an impulse response with a finite number of non-zero samplesa)Both A and R are true and R is correct explanation of Ab)Both A and R are true but R is not correct explanation of Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'D'. Can you explain this answer?
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Assertion (A): The discrete time system described by y[n] =2x[n] +4x[n-1] is unstableReason (R): It has an impulse response with a finite number of non-zero samplesa)Both A and R are true and R is correct explanation of Ab)Both A and R are true but R is not correct explanation of Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Assertion (A): The discrete time system described by y[n] =2x[n] +4x[n-1] is unstableReason (R): It has an impulse response with a finite number of non-zero samplesa)Both A and R are true and R is correct explanation of Ab)Both A and R are true but R is not correct explanation of Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): The discrete time system described by y[n] =2x[n] +4x[n-1] is unstableReason (R): It has an impulse response with a finite number of non-zero samplesa)Both A and R are true and R is correct explanation of Ab)Both A and R are true but R is not correct explanation of Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'D'. Can you explain this answer?.
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