Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > Comment on the time invariance of the followi...
Start Learning for Free
Comment on the time invariance of the following discrete system: y[n] = x[2n+4].
- a)Time invariant
- b)Time variant
- c)Both Time variant and Time invariant
- d)None of the mentioned
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Comment on the time invariance of the following discrete system: y[n] ...
A time shift in the input scale gives double the time shift in the output scale, and hence is time variant.
Most Upvoted Answer
Comment on the time invariance of the following discrete system: y[n] ...
Time Invariance of a Discrete System:
A discrete system is said to be time-invariant if its output depends only on the present and past values of the input signal, and not on the time at which the input is applied. In other words, if a time shift is applied to the input signal, the output signal should also undergo the same time shift.
In the given system, y[n] = x[2n+4], we can see that the output depends on the input signal at a shifted time instant.
Explanation:
Let us consider two input signals, x1[n] and x2[n], such that x1[n] = x2[n] for all n.
Now, let us apply a time shift of k samples to both input signals, such that x1[n-k] and x2[n-k] are the new input signals.
For the given system to be time-invariant, the output signals y1[n] and y2[n] corresponding to x1[n-k] and x2[n-k] should be identical to the output signals y1[n-k] and y2[n-k] corresponding to the original input signals x1[n] and x2[n].
y1[n-k] = x1[2(n-k)+4] = x1[2n-2k+4]
y2[n-k] = x2[2(n-k)+4] = x2[2n-2k+4]
y1[n] = x1[2n+4]
y2[n] = x2[2n+4]
Now, if we compare y1[n-k] and y2[n-k] with y1[n] and y2[n], we can see that they are not identical. This is because the output signal depends on the value of n, and a time shift of k samples in the input signal results in a different value of n.
Therefore, the given system is time-variant.
Conclusion:
The given discrete system, y[n] = x[2n+4], is time-variant as the output signal depends on the time at which the input is applied.
A discrete system is said to be time-invariant if its output depends only on the present and past values of the input signal, and not on the time at which the input is applied. In other words, if a time shift is applied to the input signal, the output signal should also undergo the same time shift.
In the given system, y[n] = x[2n+4], we can see that the output depends on the input signal at a shifted time instant.
Explanation:
Let us consider two input signals, x1[n] and x2[n], such that x1[n] = x2[n] for all n.
Now, let us apply a time shift of k samples to both input signals, such that x1[n-k] and x2[n-k] are the new input signals.
For the given system to be time-invariant, the output signals y1[n] and y2[n] corresponding to x1[n-k] and x2[n-k] should be identical to the output signals y1[n-k] and y2[n-k] corresponding to the original input signals x1[n] and x2[n].
y1[n-k] = x1[2(n-k)+4] = x1[2n-2k+4]
y2[n-k] = x2[2(n-k)+4] = x2[2n-2k+4]
y1[n] = x1[2n+4]
y2[n] = x2[2n+4]
Now, if we compare y1[n-k] and y2[n-k] with y1[n] and y2[n], we can see that they are not identical. This is because the output signal depends on the value of n, and a time shift of k samples in the input signal results in a different value of n.
Therefore, the given system is time-variant.
Conclusion:
The given discrete system, y[n] = x[2n+4], is time-variant as the output signal depends on the time at which the input is applied.
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
|
|
Similar Electrical Engineering (EE) Doubts
Top Courses for Electrical Engineering (EE)View all
Comment on the time invariance of the following discrete system: y[n] = x[2n+4].a)Time invariantb)Time variantc)Both Time variant and Time invariantd)None of the mentionedCorrect answer is option 'B'. Can you explain this answer?
Question Description
Comment on the time invariance of the following discrete system: y[n] = x[2n+4].a)Time invariantb)Time variantc)Both Time variant and Time invariantd)None of the mentionedCorrect answer is option 'B'. 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 Comment on the time invariance of the following discrete system: y[n] = x[2n+4].a)Time invariantb)Time variantc)Both Time variant and Time invariantd)None of the mentionedCorrect answer is option 'B'. 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 Comment on the time invariance of the following discrete system: y[n] = x[2n+4].a)Time invariantb)Time variantc)Both Time variant and Time invariantd)None of the mentionedCorrect answer is option 'B'. Can you explain this answer?.
Comment on the time invariance of the following discrete system: y[n] = x[2n+4].a)Time invariantb)Time variantc)Both Time variant and Time invariantd)None of the mentionedCorrect answer is option 'B'. 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 Comment on the time invariance of the following discrete system: y[n] = x[2n+4].a)Time invariantb)Time variantc)Both Time variant and Time invariantd)None of the mentionedCorrect answer is option 'B'. 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 Comment on the time invariance of the following discrete system: y[n] = x[2n+4].a)Time invariantb)Time variantc)Both Time variant and Time invariantd)None of the mentionedCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Comment on the time invariance of the following discrete system: y[n] = x[2n+4].a)Time invariantb)Time variantc)Both Time variant and Time invariantd)None of the mentionedCorrect answer is option 'B'. 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 Comment on the time invariance of the following discrete system: y[n] = x[2n+4].a)Time invariantb)Time variantc)Both Time variant and Time invariantd)None of the mentionedCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Comment on the time invariance of the following discrete system: y[n] = x[2n+4].a)Time invariantb)Time variantc)Both Time variant and Time invariantd)None of the mentionedCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Comment on the time invariance of the following discrete system: y[n] = x[2n+4].a)Time invariantb)Time variantc)Both Time variant and Time invariantd)None of the mentionedCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Comment on the time invariance of the following discrete system: y[n] = x[2n+4].a)Time invariantb)Time variantc)Both Time variant and Time invariantd)None of the mentionedCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Comment on the time invariance of the following discrete system: y[n] = x[2n+4].a)Time invariantb)Time variantc)Both Time variant and Time invariantd)None of the mentionedCorrect answer is option 'B'. 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup