fourier parameters
- To: mathgroup at smc.vnet.net
- Subject: [mg102874] fourier parameters
- From: rip pelletier <bitbucket at comcast.net>
- Date: Tue, 1 Sep 2009 03:51:20 -0400 (EDT)
hi,
I take the following Sinc^2 function:
F[s_]=1/5 Sinc[Pi s/5]^2
and i execute two alternatives.
one, i ask for the
f[t_]=InverseFourierTransform[F[s],s,t,FourierParameters->{0,-2Pi}]//Expa
nd
This gives me a triangle of width 0.4, centered at the origin, of height
1:
-(1/2) Sign[-(1/5)+t]+5/2 t Sign[-(1/5)+t]-5 t Sign[t]+1/2
Sign[1/5+t]+5/2 t Sign[1/5+t]
two, having read the documentation on FourierParameters, I compute the
integral explicitly. As i read the documentation, the factor in front of
the integral is 1.
Assuming[t\[Element]Reals,\!\(
\*UnderoverscriptBox[\(\[Integral]\), \(-\[Infinity]\),
\(\[Infinity]\)]\(F[s] E^\((2\ Pi\ I\ s\ t)\) \[DifferentialD]s\)\)]
Once again, i get a triangle of width .4, centered at the origin.
1/5 If[t^2<25 t^4,0,5/2 (1-5 Abs[t])]
but its height is 1/2.
am i doing something wrong?
in case it matters, i'm running mathematica 7.0.1.0 on OS X 10.5.8
(leopard).
vale,
rip
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