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I Proving Fourier Transform

  1. Apr 17, 2016 #1
    fourierSeries.png
    Quote: "The Fourier transform is a generalization of the complexFourier series in the limit as [PLAIN]http://mathworld.wolfram.com/images/equations/FourierTransform/Inline1.gif. [Broken] Replace the discrete http://mathworld.wolfram.com/images/equations/FourierTransform/Inline2.gif with the continuous Inline3.gif while letting [PLAIN]http://mathworld.wolfram.com/images/equations/FourierTransform/Inline4.gif. [Broken] Then change the sum to an integral, and the equations become
    Inline5.gif Inline6.gif Inline7.gif
    (1)
    Inline8.gif Inline9.gif Inline10.gif
    "
    From: http://mathworld.wolfram.com/FourierTransform.html
    Why can we replace A(n) with F(k)dk as L tends to infinity? I know that A(n) will be continues as L tends to infinity, but I cant make sense of F(K)dk.
    Can I just let A(n)=F(k)dk or can I proof this from the definition of Fourier series rigorously?
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Apr 17, 2016 #2
    Thx I solved it.
     
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