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MathGroup Archive 1998

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Fourier Transform

  • To: mathgroup at smc.vnet.net
  • Subject: [mg13689] Fourier Transform
  • From: Edward Neuman <edneuman at siu.edu>
  • Date: Sat, 15 Aug 1998 04:39:20 -0400
  • Organization: SIUC
  • Sender: owner-wri-mathgroup at wolfram.com

Let f(x) = 1/x. If f is regarded as the generalized function, then its
Fourier transform is:
                                  -Pi*I*Sign[t] (see, e.g., G.B.
Folland, "Fourier Analysis and Its Applications," p. 337).
Using Mathematica 3.0 we get:
In[1]:=
<< "Calculus`FourierTransform`"

In[2]:=
FourierTransform[1/x, x, t]

Out[2]=
2*I*Pi*(-(1/2) + UnitStep[t, ZeroValue -> 1/2]).

This agrees with the above result only if t = 0. Bug?

Edward Neuman



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