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