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
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