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FFT, Mathematica, Continuous Fourier Transform

  1. May 14, 2009 #1
    Hi all,

    First a warning: my Mathematica skills, and computery-type skills in general, are not very hot. My problem is thus: I have a function which I know:

    [tex] \hat{f}(k) [/tex]

    I'd like mathematica to approximate the inverse fourier transform of this function for me and plot the result. I've tried using the built-in function "NInverseFourierTransform", but it fails to produce meaningful results. My function oscillates quite rapidly, so NIntegrate doesn't work too well.

    Now I'm aware that I could approximate the inverse Fourier transform using a discrete Fourier transform and the FFT algorithm - but I'm afraid I don't really know how to go about doing it. I can do the following:

    • Get as many sample points of [tex]\hat{f}(k)[/tex] as you want. Call them [tex]\{\hat{f}_n\}[/tex].
    • I can make [tex]\hat{f}[/tex] rapidly decreasing, so it's pretty much got compact support.
    • My [tex]\hat{f}[/tex] is smooth.
    I figure if I've got the above properties, there must be some way of approximating the inverse Fourier transform using the built in FFT functions in mathematica. I've tried using InverseFourier
    • , where list contains the [tex]\hat{f}_n[/tex], and plotting the real part of it, but the answer is gibberish. I've proved lots of rigorous results regarding the function [tex]f[/tex], so I know (pretty much) what the plot of the inverse Fourier transform should look like!

      If anyone could help me implement the built in mathematica functions to get a plot of this inverse Fourier transform, I'd be immensely grateful.

      Thanks,
      Ant
     
  2. jcsd
  3. May 17, 2009 #2
    All sorted now - I rolled up my sleeves and got stuck into mathematica.
     
  4. Oct 29, 2010 #3
    i don't understand how fft algorithm works.
    but i have to solve the problem by Mathematica code which i have attached.
    can anybody help me to solve this function.
    it will be if any explain by a simple function.

    thanks,
    Happy
     
    Last edited: Nov 10, 2010
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