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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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