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 >