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How to Fourier transform this expression?

  1. Aug 10, 2014 #1
    I have this expression:
    [tex]f(\tau) = 4 \pi \int \omega ^2 P_2[\cos (\omega \tau)] P(\omega) \, \mathrm{d}w \quad [1][/tex] where [itex]P_2[/itex] is a second order Legendre polynomial, and [itex]P(\omega)[/itex] is some distribution function.

    Now I am told that, given a data set of [itex]f(\tau)[/itex], I can solve for [itex]P(\omega)[/itex] by either assuming a model for it or Fourier transforming Eq. [1]. I can do this by assuming a distribution, eg Gaussian, then putting it in the integral, but I do not understand how I can obtain [itex]P(\omega)[/itex] directly via Fourier transforming. How could I do this in say MATLAB or Mathematica?

    Thanks
     
  2. jcsd
  3. Aug 16, 2014 #2
    I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?
     
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