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A continuous-time input signal x (t ) is an eigen function of an LTI system, if the output is
- a)kx (t ) , where is an eigenvalue.
- b)ke jwt x (t ) , where is an eigenvalue and is a complex exponential signal.
- c)x (t ) e jwt , where e jwt is a complex exponential signal.
- d)kH (ω) , where k is an eigenvalue and H (ω) is a frequency response of the system.
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A continuous-time input signal x (t ) is an eigen function of an LTI s...
If the output signal is a scalar multiple of input signal, the signal is refereed as an eigen function (or characteristic function) and the multiplier is referred as an eigen value (or characteristic value).
If x(t) is the eigen function and k is the eigen value, then output, y(t) = kx(t).
Hence, the correct option is (A).
If x(t) is the eigen function and k is the eigen value, then output, y(t) = kx(t).
Hence, the correct option is (A).
Most Upvoted Answer
A continuous-time input signal x (t ) is an eigen function of an LTI s...
Explanation:
Analyzing the Characteristics of an LTI System:
An LTI (Linear Time-Invariant) system is characterized by two key properties: linearity and time-invariance. When an input signal x(t) is an eigenfunction of an LTI system, it means that the output signal will have a specific relationship with the input signal.
Understanding Eigenfunctions:
Eigenfunctions of a system are special input signals that, when processed by the system, result in an output signal that is proportional to the input signal. In mathematical terms, if x(t) is an eigenfunction of an LTI system, the output signal y(t) can be expressed as y(t) = kx(t), where k is the eigenvalue associated with the eigenfunction x(t).
Applying the Definition:
In the context of the given options:
a) Option A aligns with the definition of an eigenfunction for an LTI system. The output signal is directly proportional to the input signal with a scaling factor represented by the eigenvalue k. Hence, the correct statement is y(t) = kx(t).
b) Option B introduces a complex exponential signal e^jwt, which is not a characteristic of an eigenfunction for an LTI system.
c) Option C also introduces a complex exponential signal in the input, which does not align with the definition of an eigenfunction.
d) Option D involves the frequency response of the system, which is not directly related to the concept of eigenfunctions.
Conclusion:
In conclusion, the correct statement for an eigenfunction of an LTI system is y(t) = kx(t), where the output is proportional to the input with a scaling factor represented by the eigenvalue k. This relationship signifies the unique property of eigenfunctions in LTI systems.
Analyzing the Characteristics of an LTI System:
An LTI (Linear Time-Invariant) system is characterized by two key properties: linearity and time-invariance. When an input signal x(t) is an eigenfunction of an LTI system, it means that the output signal will have a specific relationship with the input signal.
Understanding Eigenfunctions:
Eigenfunctions of a system are special input signals that, when processed by the system, result in an output signal that is proportional to the input signal. In mathematical terms, if x(t) is an eigenfunction of an LTI system, the output signal y(t) can be expressed as y(t) = kx(t), where k is the eigenvalue associated with the eigenfunction x(t).
Applying the Definition:
In the context of the given options:
a) Option A aligns with the definition of an eigenfunction for an LTI system. The output signal is directly proportional to the input signal with a scaling factor represented by the eigenvalue k. Hence, the correct statement is y(t) = kx(t).
b) Option B introduces a complex exponential signal e^jwt, which is not a characteristic of an eigenfunction for an LTI system.
c) Option C also introduces a complex exponential signal in the input, which does not align with the definition of an eigenfunction.
d) Option D involves the frequency response of the system, which is not directly related to the concept of eigenfunctions.
Conclusion:
In conclusion, the correct statement for an eigenfunction of an LTI system is y(t) = kx(t), where the output is proportional to the input with a scaling factor represented by the eigenvalue k. This relationship signifies the unique property of eigenfunctions in LTI systems.
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A continuous-time input signal x (t ) is an eigen function of an LTI system, if the output isa)kx (t ) , where is an eigenvalue.b)ke jwt x (t ) , where is an eigenvalue and is a complex exponential signal.c)x (t ) e jwt , where e jwt is a complex exponential signal.d)kH (ω) , where k is an eigenvalue and H (ω) is a frequency response of the system.Correct answer is option 'A'. Can you explain this answer?
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A continuous-time input signal x (t ) is an eigen function of an LTI system, if the output isa)kx (t ) , where is an eigenvalue.b)ke jwt x (t ) , where is an eigenvalue and is a complex exponential signal.c)x (t ) e jwt , where e jwt is a complex exponential signal.d)kH (ω) , where k is an eigenvalue and H (ω) is a frequency response of the system.Correct answer is option 'A'. 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 A continuous-time input signal x (t ) is an eigen function of an LTI system, if the output isa)kx (t ) , where is an eigenvalue.b)ke jwt x (t ) , where is an eigenvalue and is a complex exponential signal.c)x (t ) e jwt , where e jwt is a complex exponential signal.d)kH (ω) , where k is an eigenvalue and H (ω) is a frequency response of the system.Correct answer is option 'A'. 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 A continuous-time input signal x (t ) is an eigen function of an LTI system, if the output isa)kx (t ) , where is an eigenvalue.b)ke jwt x (t ) , where is an eigenvalue and is a complex exponential signal.c)x (t ) e jwt , where e jwt is a complex exponential signal.d)kH (ω) , where k is an eigenvalue and H (ω) is a frequency response of the system.Correct answer is option 'A'. Can you explain this answer?.
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