Fourier Transform

  • Thread starter razorwind
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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.
 
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