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Problem with FourierTransform


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

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