Problem with FourierTransform
- To: mathgroup at smc.vnet.net
- Subject: [mg30303] Problem with FourierTransform
- From: "Oliver Friedrich" <oliver.friedrich at tz-mikroelektronik.de>
- Date: Wed, 8 Aug 2001 01:33:58 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
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