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Rule

  • To: mathgroup at smc.vnet.net
  • Subject: [mg108455] Rule
  • From: Rui <rui.rojo at gmail.com>
  • Date: Thu, 18 Mar 2010 04:33:39 -0500 (EST)

I got surprised when I saw that my Mathematica 7 computed
FourierTransform[DiracComb[t], t, f] without trouble but couldn't deal
with
FourierTransform[DiracComb[2 t], t, f]

So I thought about writing a rule that uses the property that the
F{x[k t]}[f] = 1/|k| F{x[t]}[f/k] (I think :P)

In Mathematica's words:
FourierTransform[ expr_ , t_, f_]   should be transformed, only if in
"expr" you can find aall "t"s multiplied by the same thing (let's call
it "k"), and that thing doesn't have "t"s inside, into
1/Abs[k] FourierTrnasform[expr_ (* having replaced the k t  by t *),
t, f/k]

I'm a little lost. Even if I could find a way to do it, I wanna know
how you would do it, because I'm already thinking about complicated
stuff and it doesn't seem neither a too complex or too unusual
problem.

Thanks ;)


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