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Curious problem with UnitStep

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67874] Curious problem with UnitStep
  • From: "hanspi" <hanspi at schmid-werren.ch>
  • Date: Tue, 11 Jul 2006 05:58:44 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Dear colleagues,

I am trying to calculate the ACF of a combination of unit steps and its
fourier transform.  There I see something very curious.

I do:

sw[t_, \[Tau]_] := UnitStep[\[Tau] - Abs[t]]
Plot[sw[t, 1.0], {t, -2, 2}]

which looks OK.  Then:

akf[x_, \[Tau]_] :=
  Assuming[{t \[Epsilon] Reals, \[Tau] > 0},
    Integrate[
      sw[t, \[Tau]] sw[x - t, \[Tau]], {t, -\[Infinity], \[Infinity]}]]
Plot[akf[t, 1.0], {t, -2, 2}]

Which also looks OK.

But when I just type

akf[t, 1.0]

I get as an output

2.

which is wrong, and also

FourierTransform[akf[t, 1.0], t, \[Omega]]

gives a wrong result.  Why can I plot akf properly, but not evaluate
it?

Hanspeter


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