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Fourier Transform Doubt!

  1. Mar 24, 2012 #1
    Hi
    Do Fourier Transforms give us actual amplitude/phase of the particular frequency (ejωt) just like Fourier series?
    Thanks
    Salil
     
  2. jcsd
  3. Mar 24, 2012 #2

    rbj

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    sorta, yes. but the inverse continuous Fourier transform is an integral not a summation like in the Fourier series. so the actual amplitude is proportional to the product of [itex]X(f)[/itex] and the width of the sliver of spectrum [itex] df [/itex].

    to compare, give the (inverse) Fourier integral a finite width (with the limits of the integral) and then represent that finite width integral with a Riemann summation and then you will be able to see the relationship between the inverse Fourier transform and the Fourier series. in a loose sense, they are the same thing.
     
  4. Mar 26, 2012 #3

    sophiecentaur

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    The series is a Discrete process where the Transform is Continuous. The series can yield 'wrong' / misleading results if you ignore the basic rules.
     
  5. Mar 31, 2012 #4
    what is the fourier transform of sum( Vhcos(hwt)) where h varies from 1 to infinity
     
  6. Mar 31, 2012 #5

    sophiecentaur

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    Hi
    I assume that when you write Vh , the h is a suffix.
    The transform will be a regular 'comb' of components at frequency w, hw, 2hw etc. with amplitdes given by the coefficients V. In fact, the original function is of a form that tells you the frequency spectrum just by 'observation'.
     
  7. Mar 31, 2012 #6
    http://www.infoocean.info/avatar2.jpg [Broken]The series is a Discrete process where the Transform is Continuous.
     
    Last edited by a moderator: May 5, 2017
  8. Apr 1, 2012 #7

    sophiecentaur

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    I guess I meant "sum' as against 'integral'.
    Is that better?
     
    Last edited: Apr 1, 2012
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