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MathGroup Archive 2004

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Re: Trivial Fourier Transform Question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45737] Re: [mg45729] Trivial Fourier Transform Question
  • From: "Ravinder Kumar B." <ravi at crest.ernet.in>
  • Date: Fri, 23 Jan 2004 03:15:21 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

I guess, the best thing to do it to generate a list of values of Bessel
(which is FT of your delta function) function using Table. This will be
your discrete FT representation of the analytical Bessel function. Then
you can proceed as usual to calculate Convolution.
I have not tried it earlier, so please let me also know whether it works
or not.
Regards,
Ravi




using Table with adequote number of samples.

On Thu, 22 Jan 2004, Lasse Rasmussen wrote:

> Is there an easy way to calculate the fourier series (discrete fourier
> transfrom) of a real function f(x) if I already know what the
> continuous fourier transform of f(x) is?
>
> Here is my particular application:
>
> I am doing convolutions of a 2-dimensional function f(x,y) with a
> radially symmetric dirac delta-function d(a-r), where a is a constant
> and r is just Sqrt[x^2+y^2]. I do the convolution by multiplying the
> discrete fourier transforms of my two functions. Since I only know
> f(x,y) on a grid I cannot do the convolution analytically.
>
> Obviously, it's not possible to represent a delta function discretely,
> but if I represent the dirac delta function with a very peaked
> Gaussian, I can get pretty good results, but it is not ideal. However,
> the fourier transform of my dirac delta function in 2D is just a
> Bessel function, so I was hoping to be able to calculate a very
> accurate discrete fourier transform using that knowledge. But how do I
> calculate the discrete fourier transform of a function, which fourier
> transfrom I know.
>
> Thanks,
>
> Lasse
>

-- 
    Regards,                                   Jan 22
    Ravi



         |~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~|
         |           Ravinder Kumar Banyal (SRF),                |
         |          Indian Institute of Astrophysics,            |
         |           Koramangala Bangalore - 560 034. INDIA      |
         | email : banyal at iiap.ernet.in ;   ravi at crest.ernet.in  |
         | Ph No : 080 5530672 (IIA)       080 7931972 (Hoskote) |
         |                                     7931952           |
          ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
All that is necessary for the triumph of evil is that enough good
men do nothing --Edmund Burke.


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