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MathGroup Archive 2001

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Re: Problem with FourierTransform

  • To: mathgroup at smc.vnet.net
  • Subject: [mg30350] Re: Problem with FourierTransform
  • From: Ioan Alexandre Romoscanu <romoscanu at imes.mavt.ethz.ch>
  • Date: Sat, 11 Aug 2001 03:40:14 -0400 (EDT)
  • Organization: Swiss Federal Institute of Technology (ETHZ)
  • References: <9kqjd6$4d9$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

I do not see where you could be wrong.

I also faced some quite weird Mathematica behaviour these last times (by
plotting functions...weird results, which in addition to this were different
before and after a Simplify for instance)

cheers

A.

Oliver Friedrich wrote:

> Hallo,
>
> I found some strange behaviour of FourierTransform
>
> If I multiply two sine functions and transform it with
>
> FourierTransform[Cos[a t+b]*Cos[c t+d],t,f]
>
> I get the correct answer with four DiracDeltas at a+c, a-c, -a+c, -a-d and
> some coefficients.
>
> Now the funny: If I assume both sines without a phaseshift, I can omit b and
> d and write
>
> FourierTransform[a t]*Cos[c t],t,f]
>
> FourierTransform returns my expression unevaluated. So that algorithm
> requires explicitly at least one phase shift argument. If I omit only one, I
> get a result (although I've yet not checked for correctness).
> Does anybody knows about this behaviour? At the moment my workaround is
>
> FourierTransform[Cos[a t+b]*Cos[c t+d],t,f]/.{b->0,d->0}
>
> That seems to be fair enough, but anyway, it should work without. Or didn't
> I consider some mathematical traps?
>
> Best regards
> Oliver Friedrich

--
___________________________________________
alexandre ioan romoscanu          - institut für mechanik
CLA G31, eth zentrum,            8092 zürich, schweiz
tel. +41 1 632 77 54,                     +41 76 323 63 05
fax.+41 1 632 11 45, romoscanu at imes.mavt.ethz.ch
___________________________________________




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