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Re: Problem with FourierTransform

• To: mathgroup at smc.vnet.net
• Subject: [mg30349] Re: Problem with FourierTransform
• From: "Oliver Friedrich" <oliver.friedrich at tz-mikroelektronik.de>
• Date: Sat, 11 Aug 2001 03:40:14 -0400 (EDT)
• References: <9kqjd6$4d9$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Sorry, I did a writing error, the following is the correct input. So take
look, regard the phase shift b and d

FourierTransform[Cos[a t+b]*Cos[c t+d],t,f]
works fine


FourierTransform[Cos[a t]*Cos[c t+d],t,f]
works fine

FourierTransform[Cos[a t+b]*Cos[c t],t,f]
works fine

FourierTransform[Cos[a t]*Cos[c t],t,f]
doesn't work at all

Any ideas?


"Oliver Friedrich" <oliver.friedrich at tz-mikroelektronik.de> schrieb im
Newsbeitrag news:9kqjd6$4d9$1 at smc.vnet.net...
> 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
>
>