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Trivial Fourier Transform Question

• To: mathgroup at smc.vnet.net
• Subject: [mg45729] Trivial Fourier Transform Question
• From: lasse_ras at hotmail.com (Lasse Rasmussen)
• Date: Thu, 22 Jan 2004 03:37:30 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

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

• Follow-Ups:
  • Re: Trivial Fourier Transform Question
    • From: "Sseziwa Mukasa,,(978) 536-2359" <mukasa@jeol.com>