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Re: Dirac Delta Function: Basics
*To*: mathgroup at smc.vnet.net
*Subject*: [mg75215] Re: Dirac Delta Function: Basics
*From*: dh <dh at metrohm.ch>
*Date*: Fri, 20 Apr 2007 00:46:42 -0400 (EDT)
*References*: <f07a53$4ci$1@smc.vnet.net>
Hi Gopinath,
there is a pitfall here. The Fourier sum is by definition a periodic
function. Therefore, either you restrict your domain to {-Pi,Pi} and
then you have a Delta function in your domain. Or, if your domain is
{-Infinity,Infinity} you are using a grid of Delta functions. If you
want a Delta function in this domain, you need a Fourier integral.
hope this helps, Daniel
Gopinath Venkatesan wrote:
> Hello Friends
>
> I browsed some of the previous posts in this forum on Dirac Delta function, and found some interesting distributions used to represent the delta function, at the below website:
>
> <http://mathworld.wolfram.com/DeltaFunction.html>
>
> Also when I tried using one of the distribution, Fourier series approximation (shown below), I was getting very different solutions for different entries of upper limit of k, even at higher values of upper limits.
>
> DeltaF(x - a) = 1/(2*Pi) +
> (1/Pi)*Sum[Cos[k*a]*Cos[k*x] + Sin[k*a]*Sin[k*x],
> {k, 1, Infinity}]
>
> (here DeltaF is DiracDelta).
>
> Does anyone here can give me suggestions on using right distributions and parameters. Thanks.
>
> Also Can I use the DiracDelta[] function available in Mathematica itself. How does Mathematica calculate them.
>
> I am not integrating the equation containing DiracDelta[], so as seen from the Mathematica examples, I think it is doing Laplace transformations.
>
> Any help/directions to resources are appreciated. Thanks,
>
> Gopinath
> Graduate Student
> University of Oklahoma
>
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