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Fourier Transform

  1. Jan 28, 2010 #1
    1. The problem statement, all variables and given/known data

    f(x) = {-1, -pi<x<0 ; 1, 0<x<pi ; 0, |x|>pi}

    Find the exponential Fourier transform of the given f(x) and write f(x) as a Fourier integral.

    2. Relevant equations

    3. The attempt at a solution

    I have the equations for the Fourier transforms and I know how to find the Fourier series for f(x) but I have no idea where to start this one, my book is very confusing. Can someone help me start this?
  2. jcsd
  3. Jan 28, 2010 #2


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    What is the definition of the Fourier transform you are using?
  4. Jan 28, 2010 #3


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    The Fourier transform I am familar with is
    [tex]\frac{1}{\sqrt{2\pi}}\int_{x=-\infty}^\infty f(x)e^{-isx}dx[/tex]
    If that is what you know, just go ahead and do the integration:
    [tex]\frac{1}{\sqrt{2\pi}}\left(-\int_{-\pi}^0 e^{-isx}dx+ \int_0^\pi e^{-isx}dx\right)[/tex]
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