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modifying standard representation of DiracDelta

  • To: mathgroup at smc.vnet.net
  • Subject: [mg111350] modifying standard representation of DiracDelta
  • From: Benjamin Hell <hell at exoneon.de>
  • Date: Wed, 28 Jul 2010 02:55:46 -0400 (EDT)

  Hi,
mathematica seems to have the standard representation of the DiracDelta 
function set to a*DiracDelta[1+b*f] (with a and b being complex values 
and f being the free variable). At least that is the form I get from 
using the FourierTransform (for example FourierTransform[Cos[t], t, f, 
FourierParameters -> {0, -2 Pi}]) or when just typing in DiracDelta[1/(2 
Pi) + f]. The latter Expression is transformed to 2Pi DiracDelta[1 + 2 f 
\Pi], which is a valid transformation, but not the one I would like to have.
I would prefer the standard form to be a*DiracDelta[f+b] (with a and b 
being complex values and f the free variable). So for me DiracDelta[1/(2 
Pi) + f] should stay exactly in that form and DiracDelta[1 +a*f] should 
be evaluated to 1/Abs[a]*DiracDelta[1/a + f] which is just another 
representation of the same expression. How can I achieve that 
respectively how can I implement such a rule?

Thanks in advance.


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