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