I have trouble getting started with Fouriertransforms. I have access to Mathematica but don't obtain the same results(see below).(adsbygoogle = window.adsbygoogle || []).push({});

Isn't my reasoning correct?

Example:

Fouriertransform 1/(t^2+1):

F19: e^(-a|t|),a>0 <-> 2a/(a^2+w^2)

1/(t^2+1) = 1/2 * 2/(t^2+1)

Linearity => f(t) = 1/2*g(t), g(t) = 2/(t^2+1)

Symmetry(F10)+ f19 => gtop(w) = e^-|w| * 2*Pi

=> ftop(w) = 1/2*2*Pi*e^(-|w|)

<=> ftop(w) = Pi*e^(-|w|)

Answer: ftop(w) = Pi*e^(-|w|)

But Mathematica:

FourierTransform[1/(1 + t^2), t, \[Omega]]

E^-Abs[\[Omega]] Sqrt[\[Pi]/2]

Where does the root come from?

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# Probelm getting started with Fouriertransforms!

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