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Re: FourierTransform of a function defined in sections
*To*: mathgroup at smc.vnet.net
*Subject*: [mg70189] Re: FourierTransform of a function defined in sections
*From*: Paul Abbott <paul at physics.uwa.edu.au>
*Date*: Sat, 7 Oct 2006 07:06:59 -0400 (EDT)
*Organization*: The University of Western Australia
*References*: <eg4soa$ffu$1@smc.vnet.net>
In article <eg4soa$ffu$1 at smc.vnet.net>,
"Eckhard Schlemm" <e.schlemm at hotmail.de> wrote:
> I want Mathematica to calculate the FourierTransform of a function which is
> defined by Sin[x]^2 for Abs[x]<PI and zero else.
What version of Mathematica are you using? For Piecewise functions, it
is preferable to use Piecewise.
> I tried and defined the function g as follows:
>
> g[x_]:=If[Abs[x]>PI,0,Sin[x]^2];
I assume that you have Pi instead of PI.
> That works fine.
Note that in version 5.2, PiecewiseExpand converts g[x] to a Piecewise
function -- and such operations are done automatically, if required. For
example,
Integrate[g[x], x]
yields
Piecewise[{{x/2 - Sin[2 x]/4, Abs[x] <= Pi}}, 0]
> But if I have mathematica try to determine the FourierTransform by
>
> FourierTransform[g[x],x,p]
>
> I always get the error that the recursion limit and the iteration limit were
> exceeded...
>
> what am I'm doing wrong?
In version 5.2 the following three expressions are identical:
FourierTransform[g[x], x, k]
FourierTransform[Piecewise[{{Sin[x]^2, -Pi <= x <= Pi}}], x, k]
1/Sqrt[2 Pi] Integrate[E^(I k x) Sin[x]^2, {x, -Pi, Pi}]
Cheers,
Paul
_______________________________________________________________________
Paul Abbott Phone: 61 8 6488 2734
School of Physics, M013 Fax: +61 8 6488 1014
The University of Western Australia (CRICOS Provider No 00126G)
AUSTRALIA http://physics.uwa.edu.au/~paul
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