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>

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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