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MathGroup Archive 2001

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Re: Re: Problem with FourierTransform

  • To: mathgroup at
  • Subject: [mg30367] Re: [mg30349] Re: Problem with FourierTransform
  • From: BobHanlon at
  • Date: Sun, 12 Aug 2001 02:29:55 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

In a message dated 2001/8/11 4:27:07 AM, 
oliver.friedrich at writes:

>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?

Evaluates on my system


"4.1 for Power Macintosh (November 2, 2000)"

(FourierTransform[Cos[a t+b]*Cos[c t+d],t,f] /. {b -> 0, d -> 0})== 
  FourierTransform[Cos[a t]*Cos[c t],t,f]


You might try using TrigReduce prior to transforming

Factor[FourierTransform[TrigReduce[Cos[a t] Cos[c t]],t,f]]

(1/2)*Sqrt[Pi/2]*(DiracDelta[a - c - f] + 
   DiracDelta[a + c - f] + DiracDelta[a - c + f] + 
   DiracDelta[a + c + f])

Bob Hanlon
Chantilly, VA  USA

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