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Homework Help: Fourier Transform

  1. Feb 1, 2009 #1
    Determine the Fourier transform of the following signals: [tex]x(t) = \frac{1}{(1+t^2)}[/tex]

    I start off by doing [tex]X(f) = \int{x(t)*e^{-j2\pi{}ft} dt}[/tex]

    So i plug in x(t) into that equation, but i'm lost as to how to integrate it. Am i going in the right direction?

    Also: x(t)=abs(t) for [tex]-2\leq{}t\leq{}2[/tex]

    I am splitting it to -t for [tex]-2\leq{}t\leq{}0[/tex] and t for [tex]0\leq{}t\leq{}2[/tex] then doing the transform with the equation above. Is it allowed to split it into 2 integrals? So it ends up being [tex]X(f) = \int{-t*e^{-j2\pi{}ft} dt}[/tex] + [tex]\int{t*e^{-j2\pi{}ft} dt}[/tex] and I simplify from there.
    Last edited: Feb 1, 2009
  2. jcsd
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