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Re: FoourierTransform of a function defined in sections


You could work as follows:

$VersionNumber
5.2

FourierTransform[hh[x], x, s]
-((2*Sqrt[2/Pi]*Sin[Pi*s])/(-4*s + s^3))

or

(1/Sqrt[2*Pi])*Integrate[hh[x]*Exp[I*s*x], {x, -Infinity, Infinity}]
-((2*Sqrt[2/Pi]*Sin[Pi*s])/(s*(-4 + s^2)))

In either case

N[%] /. s -> 1/2
0.8510768648563898

(*check*)

Chop[(1/Sqrt[2*Pi])*NIntegrate[hh[x]*Exp[I*(1/2)*x], {x, -Infinity,
Infinity}]]
0.8510768648563899


Cheers


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