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MathGroup Archive 2006

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Re: FoourierTransform of a function defined in sections

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70192] Re: FoourierTransform of a function defined in sections
  • From: dimmechan at yahoo.com
  • Date: Sat, 7 Oct 2006 07:07:09 -0400 (EDT)
  • References: <eg4soa$ffu$1@smc.vnet.net>

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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