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MathGroup Archive 2010

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DiracComb and Fouriertransform

  • To: mathgroup at smc.vnet.net
  • Subject: [mg111563] DiracComb and Fouriertransform
  • From: Benjamin Hell <hell at exoneon.de>
  • Date: Thu, 5 Aug 2010 07:00:45 -0400 (EDT)

  Hi,
Mathematica 7 seems to have great problems calculating the 
Fouriertransform of expressions involving the DiracComb. Whilst 
Mathematica is able to compute the Fouriertransform of the DiracComb, 
which is the DiracComb itself, without any further ado, even a slight 
change to the DiracComb distribution makes Mathematica stumble:
FourierTransform[DiracComb[t], t, f, FourierParameters -> {0, -2 Pi}] 
delivers DiracComb[f], which is correct.
But
FourierTransform[DiracComb[2*t], t, f, FourierParameters -> {0, -2 Pi}] 
seems to be too much to handle for mathematica, which is really strange, 
because this would be an easy application for applying some basic 
Fouriertransformation rules.
If f[t] is an arbitrary function, which can be transformed using the 
Fouriertransform, mathematica is not able to calculate the following:
FourierTransform[f[t]*DiracComb[t], t, f, FourierParameters -> {0, -2 Pi}]
Calculating the result is an easy application of the linearity of the 
Fouriertransform and the definition of the DiracComb respectively the 
DiracDelta function.

So, is there an convenient way to make mathematica calculate the above 
examples correctly? (implementing new rules seems to be quite tricky here)

Btw: I use the Fouriertransform for signalprocessing, hence the 
Fourierparameters option. This has of course no impact on mathematica 
succeeding in calculating the Fouriertransform.

Thanks in advance.


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