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Re: FoourierTransform of a function defined in sections
*To*: mathgroup at smc.vnet.net
*Subject*: [mg70196] Re: FoourierTransform of a function defined in sections
*From*: dimmechan at yahoo.com
*Date*: Sat, 7 Oct 2006 07:07:24 -0400 (EDT)
*References*: <eg4soa$ffu$1@smc.vnet.net>
Hello.
On version 5.1 and newer you can work as follows:
Clear[hh]
hh[x_] := Piecewise[{{Sin[x]^2, Abs[x] <= Pi}, {0, x > Pi || x < Pi}}]
Here is its plot
Plot[hh[x], {x, -4, 4}]
Here is the FT
FourierTransform[hh[x], x, s]
-((2*Sqrt[2/Pi]*Sin[Pi*s])/(-4*s + s^3))
Here is the numrical value for s=1/2
N[% /. s -> 1/2]
0.8510768648563898
Here is the check
Chop[NIntegrate[(1/Sqrt[2*Pi])*hh[x]*Exp[I*s*x] /. s -> 1/2, {x,
-Infinity, Infinity}]]
0.8510768648563898
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