Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > Assertion (A): The discrete time system descr...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
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.
Attention Electrical Engineering (EE) Students!
To make sure you are not studying endlessly, EduRev has designed Electrical Engineering (EE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Electrical Engineering (EE).
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Top Courses for Electrical Engineering (EE)View all
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?
Question Description
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?.
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?.
Solutions 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? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice Electrical Engineering (EE) tests.
|
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup