Numerical Differentiation using Fourier Transform

*To*: mathgroup at smc.vnet.net*Subject*: [mg32941] Numerical Differentiation using Fourier Transform*From*: m.p.croucher at sheffield.ac.uk (Mike)*Date*: Wed, 20 Feb 2002 01:26:25 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hi I need to differentiate a function that i only know numerically and for various reasons I have been asked to do this via a Fourier Transform Method. Before doing it on the horrible function I am dealing with, I thought I would get to grips with the method using much easier functions. So say I want to differentiate E^(-x^2) w.r.t x using Fourier Transforms : analytically i could proceed as follows FourierTransform[E^(-x^2), x, w]] = 1/(Sqrt[2]*E^(w^2/4)) multiply this by I*w and taking the inverse Transform yields (-2*x)/E^x^2 as expected so i am along the right lines here. Now I assume that I only know this function numerically and see if i can reproduce this result. First I made a table of values : test = Table[E^(-x^2), {x, 0.01, 20, 0.01}]; and find it's DFT using Fourier[test] now in order to find the derivative I need to multiply this by I*w and take the inverse transform. My problem is how to do this? what are my values of w? The DFT looks very different to the one I found analytically and to be honest I don't have a clue of whats going on. Any help would be appreciated - Thanks Mike

**Follow-Ups**:**Re: Numerical Differentiation using Fourier Transform***From:*Sseziwa Mukasa <mukasa@jeol.com>