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Fourier Transform

  1. Dec 3, 2005 #1
    How can I prove that doing a Fourier transform on a function f(x) twice gives back f(-x)?

  2. jcsd
  3. Dec 3, 2005 #2


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    I think you're asking about the double integral

    [tex]\int_{-\infty}^{\infty} e^{i kx} dk \int_{-\infty}^{\infty}e^{ikx'} f(x')dx'[/tex]

    If so, then the outer integral

    [tex]\int_{-\infty}^{\infty}e^{i k (x+x')} dk = \delta (x+x')[/tex]

    i.e. the Dirac delta function and you arrive at your result upon evaluating the inner integral. (That's ignoring factors of [itex]2\pi[/itex] which I am sure you can handle!)
    Last edited: Dec 3, 2005
  4. Dec 3, 2005 #3
    I should hope so. Thanks!
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