Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > If the Eigen function of an LTI system is x(n...
Start Learning for Free
If the Eigen function of an LTI system is x(n)= Aejnπ and the impulse response of the system is h(n)=(1/2)nu(n), then what is the Eigen value of the system?
- a)3/2
- b)-3/2
- c)-2/3
- d)2/3
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If the Eigen function of an LTI system is x(n)= Aejnπand the impuls...
Explanation: First we evaluate the Fourier transform of the impulse response of the system h(n)
If the input signal is a complex exponential signal, then the input is known as Eigen function and H(ω) is called the Eigen value of the system. So, the Eigen value of the system mentioned above is 2/3.
Most Upvoted Answer
If the Eigen function of an LTI system is x(n)= Aejnπand the impuls...
If the eigenfunction of an LTI (Linear Time-Invariant) system is given by x(n) = A * e^(jn), where A is a constant and n is the discrete time index, we can analyze the system's response to this eigenfunction.
To determine the system's output, we can substitute the eigenfunction into the LTI system's input-output equation. Let's assume the system's input-output equation is given by y(n) = H{x(n)}, where H represents the system's impulse response.
Substituting the eigenfunction into the input-output equation, we get y(n) = H{A * e^(jn)}.
Since the system is linear, we can factor out the constant A: y(n) = A * H{e^(jn)}.
Now, we need to determine the effect of the exponential term e^(jn) on the system's output. This will depend on the specific system's impulse response.
If the system is time-invariant, its impulse response will not depend on the specific time instance n. In this case, we can simplify the equation to y(n) = A * H{e^(jn)} = A * H * e^(jn).
However, if the system is not time-invariant and its impulse response depends on the specific time instance, the equation will be more complex and may involve different terms for different time instances.
Overall, the specific form and behavior of the system's output y(n) will depend on the impulse response H of the LTI system. Without knowing the impulse response, we cannot determine the exact output behavior.
To determine the system's output, we can substitute the eigenfunction into the LTI system's input-output equation. Let's assume the system's input-output equation is given by y(n) = H{x(n)}, where H represents the system's impulse response.
Substituting the eigenfunction into the input-output equation, we get y(n) = H{A * e^(jn)}.
Since the system is linear, we can factor out the constant A: y(n) = A * H{e^(jn)}.
Now, we need to determine the effect of the exponential term e^(jn) on the system's output. This will depend on the specific system's impulse response.
If the system is time-invariant, its impulse response will not depend on the specific time instance n. In this case, we can simplify the equation to y(n) = A * H{e^(jn)} = A * H * e^(jn).
However, if the system is not time-invariant and its impulse response depends on the specific time instance, the equation will be more complex and may involve different terms for different time instances.
Overall, the specific form and behavior of the system's output y(n) will depend on the impulse response H of the LTI system. Without knowing the impulse response, we cannot determine the exact output behavior.
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
If the Eigen function of an LTI system is x(n)= Aejnπand the impulse response of the system is h(n)=(1/2)nu(n), then what is the Eigen value of the system?a)3/2b)-3/2c)-2/3d)2/3Correct answer is option 'D'. Can you explain this answer?
Question Description
If the Eigen function of an LTI system is x(n)= Aejnπand the impulse response of the system is h(n)=(1/2)nu(n), then what is the Eigen value of the system?a)3/2b)-3/2c)-2/3d)2/3Correct 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 If the Eigen function of an LTI system is x(n)= Aejnπand the impulse response of the system is h(n)=(1/2)nu(n), then what is the Eigen value of the system?a)3/2b)-3/2c)-2/3d)2/3Correct 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 If the Eigen function of an LTI system is x(n)= Aejnπand the impulse response of the system is h(n)=(1/2)nu(n), then what is the Eigen value of the system?a)3/2b)-3/2c)-2/3d)2/3Correct answer is option 'D'. Can you explain this answer?.
If the Eigen function of an LTI system is x(n)= Aejnπand the impulse response of the system is h(n)=(1/2)nu(n), then what is the Eigen value of the system?a)3/2b)-3/2c)-2/3d)2/3Correct 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 If the Eigen function of an LTI system is x(n)= Aejnπand the impulse response of the system is h(n)=(1/2)nu(n), then what is the Eigen value of the system?a)3/2b)-3/2c)-2/3d)2/3Correct 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 If the Eigen function of an LTI system is x(n)= Aejnπand the impulse response of the system is h(n)=(1/2)nu(n), then what is the Eigen value of the system?a)3/2b)-3/2c)-2/3d)2/3Correct answer is option 'D'. Can you explain this answer?.
Solutions for If the Eigen function of an LTI system is x(n)= Aejnπand the impulse response of the system is h(n)=(1/2)nu(n), then what is the Eigen value of the system?a)3/2b)-3/2c)-2/3d)2/3Correct 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 If the Eigen function of an LTI system is x(n)= Aejnπand the impulse response of the system is h(n)=(1/2)nu(n), then what is the Eigen value of the system?a)3/2b)-3/2c)-2/3d)2/3Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the Eigen function of an LTI system is x(n)= Aejnπand the impulse response of the system is h(n)=(1/2)nu(n), then what is the Eigen value of the system?a)3/2b)-3/2c)-2/3d)2/3Correct answer is option 'D'. Can you explain this answer?, a detailed solution for If the Eigen function of an LTI system is x(n)= Aejnπand the impulse response of the system is h(n)=(1/2)nu(n), then what is the Eigen value of the system?a)3/2b)-3/2c)-2/3d)2/3Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of If the Eigen function of an LTI system is x(n)= Aejnπand the impulse response of the system is h(n)=(1/2)nu(n), then what is the Eigen value of the system?a)3/2b)-3/2c)-2/3d)2/3Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the Eigen function of an LTI system is x(n)= Aejnπand the impulse response of the system is h(n)=(1/2)nu(n), then what is the Eigen value of the system?a)3/2b)-3/2c)-2/3d)2/3Correct 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