FourierTransform

• To: mathgroup at smc.vnet.net
• Subject: [mg24546] FourierTransform
• From: "Rasmus Debitsch" <debitsch at Zeiss.de>
• Date: Mon, 24 Jul 2000 03:04:25 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello MathGroup,

I'm trying to compute the Fourier transform of cos[a + t] and get the result
0 :

Clear[a, t, s];
FourierTransform[Sin[t + a], t, s]
Out[67]=  0

Splitting the expression and computing the single terms gives :

In[68]:=  Sin[t + a] // TrigExpand
Out[68]=  Cos[t] Sin[a] + Cos[a] Sin[t]
In[69]:=  Clear[a, t, s];
FourierTransform[Cos[t] Sin[b], t, s] +
FourierTransform[Cos[b] Sin[t], t, s]

Out[70]=  Cos[b]*(I*Sqrt[Pi/2]*DiracDelta[s - 1] -
I*Sqrt[Pi/2]*DiracDelta[s + 1]) +
(Sqrt[Pi/2]*DiracDelta[s - 1] +
Sqrt[Pi/2]*DiracDelta[s + 1])*Sin[b]

which is the expected result. What's wrong with my first try ?

Regards
Rasmus

--

Rasmus Debitsch
Carl Zeiss Lithos GmbH
Carl Zeiss Strasse
D-73447 Oberkochen

eMail : debitsch at zeiss.de

```

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