- #1
toofle
- 20
- 0
I have trouble getting started with Fouriertransforms. I have access to Mathematica but don't obtain the same results(see below).
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?
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?