GATE Exam  >  GATE Questions  >   Which of the following conditions are correc... Start Learning for Free
Which of the following conditions are correct for the convergence of the fourier transform of the function x(t).
1) x(t) is absolutely integrable over the range of time period.
2) x(t) should have finite number of discontinuities within any finite interval.
3) x(t) should have finite number of maxima and minima within any finite interval.
4) x(t) must be periodic.
  • a)
    1, 2, 3 & 4
  • b)
    1, 2 & 4 only
  • c)
    1, 3 & 4 only
  • d)
    1, 2 & 3 only
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Which of the following conditions are correct for the convergence of ...
Dirichlet’s Conditions
The conditions under which a periodic function f(t) can be expanded in a convergent Fourier Series, are known as Dirichlet’s conditions. These are as follows:
i) f(t) is a single-valued function.
ii) f(t) has a finite number of discontinuities in each period T.
iii) f(t) has a finite number of Maxima & Minima in each period T.
iv) The Integral exists and is finite or in other way,
1, 2 & 3 are the Dirichlet conditions.
Periodicity is not the necessary condition for the convergence of Fourier transform. Since an a periodic signal may be looked at as a periodic signal with an infinite period. Note what follows is not a mathematically rigorous exercise, but will help develop an intuition for the Fourier Transform for a periodic signals.
View all questions of this test
Most Upvoted Answer
Which of the following conditions are correct for the convergence of ...
A)1, 2
Explore Courses for GATE exam
Which of the following conditions are correct for the convergence of the fourier transform of the function x(t).1) x(t) is absolutely integrable over the range of time period.2) x(t) should have finite number of discontinuities within any finite interval.3) x(t) should have finite number of maxima and minima within any finite interval.4) x(t) must be periodic.a)1, 2, 3 & 4b)1, 2 & 4 onlyc)1, 3 & 4 onlyd)1, 2 & 3 onlyCorrect answer is option 'D'. Can you explain this answer?
Question Description
Which of the following conditions are correct for the convergence of the fourier transform of the function x(t).1) x(t) is absolutely integrable over the range of time period.2) x(t) should have finite number of discontinuities within any finite interval.3) x(t) should have finite number of maxima and minima within any finite interval.4) x(t) must be periodic.a)1, 2, 3 & 4b)1, 2 & 4 onlyc)1, 3 & 4 onlyd)1, 2 & 3 onlyCorrect answer is option 'D'. 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 Which of the following conditions are correct for the convergence of the fourier transform of the function x(t).1) x(t) is absolutely integrable over the range of time period.2) x(t) should have finite number of discontinuities within any finite interval.3) x(t) should have finite number of maxima and minima within any finite interval.4) x(t) must be periodic.a)1, 2, 3 & 4b)1, 2 & 4 onlyc)1, 3 & 4 onlyd)1, 2 & 3 onlyCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following conditions are correct for the convergence of the fourier transform of the function x(t).1) x(t) is absolutely integrable over the range of time period.2) x(t) should have finite number of discontinuities within any finite interval.3) x(t) should have finite number of maxima and minima within any finite interval.4) x(t) must be periodic.a)1, 2, 3 & 4b)1, 2 & 4 onlyc)1, 3 & 4 onlyd)1, 2 & 3 onlyCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Which of the following conditions are correct for the convergence of the fourier transform of the function x(t).1) x(t) is absolutely integrable over the range of time period.2) x(t) should have finite number of discontinuities within any finite interval.3) x(t) should have finite number of maxima and minima within any finite interval.4) x(t) must be periodic.a)1, 2, 3 & 4b)1, 2 & 4 onlyc)1, 3 & 4 onlyd)1, 2 & 3 onlyCorrect answer is option 'D'. 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 Which of the following conditions are correct for the convergence of the fourier transform of the function x(t).1) x(t) is absolutely integrable over the range of time period.2) x(t) should have finite number of discontinuities within any finite interval.3) x(t) should have finite number of maxima and minima within any finite interval.4) x(t) must be periodic.a)1, 2, 3 & 4b)1, 2 & 4 onlyc)1, 3 & 4 onlyd)1, 2 & 3 onlyCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Which of the following conditions are correct for the convergence of the fourier transform of the function x(t).1) x(t) is absolutely integrable over the range of time period.2) x(t) should have finite number of discontinuities within any finite interval.3) x(t) should have finite number of maxima and minima within any finite interval.4) x(t) must be periodic.a)1, 2, 3 & 4b)1, 2 & 4 onlyc)1, 3 & 4 onlyd)1, 2 & 3 onlyCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Which of the following conditions are correct for the convergence of the fourier transform of the function x(t).1) x(t) is absolutely integrable over the range of time period.2) x(t) should have finite number of discontinuities within any finite interval.3) x(t) should have finite number of maxima and minima within any finite interval.4) x(t) must be periodic.a)1, 2, 3 & 4b)1, 2 & 4 onlyc)1, 3 & 4 onlyd)1, 2 & 3 onlyCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Which of the following conditions are correct for the convergence of the fourier transform of the function x(t).1) x(t) is absolutely integrable over the range of time period.2) x(t) should have finite number of discontinuities within any finite interval.3) x(t) should have finite number of maxima and minima within any finite interval.4) x(t) must be periodic.a)1, 2, 3 & 4b)1, 2 & 4 onlyc)1, 3 & 4 onlyd)1, 2 & 3 onlyCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Which of the following conditions are correct for the convergence of the fourier transform of the function x(t).1) x(t) is absolutely integrable over the range of time period.2) x(t) should have finite number of discontinuities within any finite interval.3) x(t) should have finite number of maxima and minima within any finite interval.4) x(t) must be periodic.a)1, 2, 3 & 4b)1, 2 & 4 onlyc)1, 3 & 4 onlyd)1, 2 & 3 onlyCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice GATE tests.
Explore Courses for GATE exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev