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