GATE Exam > GATE Questions > The Fourier transform of a signal h(t) is H(j...
Start Learning for Free
The Fourier transform of a signal h(t) is H(jω) = (2 cosω) (sin2ω)/ω. The value of
h(0) is
h(0) is
- a)1/4
- b)1/2
- c)1
- d)2
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The Fourier transform of a signal h(t) is H(jω) = (2 cosω)...
We know that inverse Fourier transform of sin c function is a rectangular function.
Most Upvoted Answer
The Fourier transform of a signal h(t) is H(jω) = (2 cosω)...
Ω), where ω is the frequency domain variable. The Fourier transform is a mathematical transformation that converts a signal from the time domain to the frequency domain. In the frequency domain, the signal is represented as a sum of sinusoidal components with different frequencies, amplitudes, and phases.
The Fourier transform is defined as:
H(jω) = ∫h(t)e^(-jωt)dt
where j = √(-1) is the imaginary unit, ω is the angular frequency in radians per second, and the integral is taken over all time t.
The Fourier transform is a complex function of ω, which means it has both real and imaginary components. The magnitude of the Fourier transform, |H(jω)|, represents the amplitude of the sinusoidal components at each frequency, while the phase of the Fourier transform, arg(H(jω)), represents the phase shift of each component.
The inverse Fourier transform is used to convert the signal back from the frequency domain to the time domain:
h(t) = (1/2π) ∫H(jω)e^(jωt)dω
where the integral is taken over all frequencies ω. The inverse Fourier transform is also a complex function of time t, and it can be used to reconstruct the original signal from its frequency components.
The Fourier transform is defined as:
H(jω) = ∫h(t)e^(-jωt)dt
where j = √(-1) is the imaginary unit, ω is the angular frequency in radians per second, and the integral is taken over all time t.
The Fourier transform is a complex function of ω, which means it has both real and imaginary components. The magnitude of the Fourier transform, |H(jω)|, represents the amplitude of the sinusoidal components at each frequency, while the phase of the Fourier transform, arg(H(jω)), represents the phase shift of each component.
The inverse Fourier transform is used to convert the signal back from the frequency domain to the time domain:
h(t) = (1/2π) ∫H(jω)e^(jωt)dω
where the integral is taken over all frequencies ω. The inverse Fourier transform is also a complex function of time t, and it can be used to reconstruct the original signal from its frequency components.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
The Fourier transform of a signal h(t) is H(jω) = (2 cosω) (sin2ω)/ω. The value ofh(0) isa)1/4b)1/2c)1d)2Correct answer is option 'C'. Can you explain this answer?
Question Description
The Fourier transform of a signal h(t) is H(jω) = (2 cosω) (sin2ω)/ω. The value ofh(0) isa)1/4b)1/2c)1d)2Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The Fourier transform of a signal h(t) is H(jω) = (2 cosω) (sin2ω)/ω. The value ofh(0) isa)1/4b)1/2c)1d)2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Fourier transform of a signal h(t) is H(jω) = (2 cosω) (sin2ω)/ω. The value ofh(0) isa)1/4b)1/2c)1d)2Correct answer is option 'C'. Can you explain this answer?.
The Fourier transform of a signal h(t) is H(jω) = (2 cosω) (sin2ω)/ω. The value ofh(0) isa)1/4b)1/2c)1d)2Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The Fourier transform of a signal h(t) is H(jω) = (2 cosω) (sin2ω)/ω. The value ofh(0) isa)1/4b)1/2c)1d)2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Fourier transform of a signal h(t) is H(jω) = (2 cosω) (sin2ω)/ω. The value ofh(0) isa)1/4b)1/2c)1d)2Correct answer is option 'C'. Can you explain this answer?.
Solutions for The Fourier transform of a signal h(t) is H(jω) = (2 cosω) (sin2ω)/ω. The value ofh(0) isa)1/4b)1/2c)1d)2Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of The Fourier transform of a signal h(t) is H(jω) = (2 cosω) (sin2ω)/ω. The value ofh(0) isa)1/4b)1/2c)1d)2Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The Fourier transform of a signal h(t) is H(jω) = (2 cosω) (sin2ω)/ω. The value ofh(0) isa)1/4b)1/2c)1d)2Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The Fourier transform of a signal h(t) is H(jω) = (2 cosω) (sin2ω)/ω. The value ofh(0) isa)1/4b)1/2c)1d)2Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The Fourier transform of a signal h(t) is H(jω) = (2 cosω) (sin2ω)/ω. The value ofh(0) isa)1/4b)1/2c)1d)2Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The Fourier transform of a signal h(t) is H(jω) = (2 cosω) (sin2ω)/ω. The value ofh(0) isa)1/4b)1/2c)1d)2Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE 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