Fourier transform
- To: mathgroup at smc.vnet.net
- Subject: [mg16238] Fourier transform
- From: "Kevin Jaffe" <kj0 at mailcity.com>
- Date: Fri, 5 Mar 1999 00:41:04 -0500
- Organization: MailCity (http://www.mailcity.lycos.com:80)
- Sender: owner-wri-mathgroup at wolfram.com
Hi. I'm getting weird results with the Calculus'Fourier Transform' package. For example, let f be a normal probability density distribution with zero mean and unit variance, and let g be a square "bump" (g(x) = 1 if |x| < 1/2, g(x) = 0 otherwise; actually, I define it using a sum of two suitable UnitStep functions, from Calculus'DiracDelta'); let F and G be the functions obtained by applying FourierTransform to f and g respectively, and let h be the function obtained by applying InverseFourierTransform to the product of F and G. The result should be the convolution f*g of f and g. But when I plot the resulting function h, I get a graph that looks nothing like the convolution f*g (which I can compute explicitly, if laboriously). Am I doing something wrong? (If instead I apply the built-in Fourier and InverseFourier to suitably constructed arrays, the resulting function does look qualitatively like f*g. But, since the output of InverseFourier is an array of numbers, namely, evenly spaced ordinate values of the inverse transform, how does one determine the actual abscissa values?) (This is all done on $Version "Silicon Graphics 3.0 (April 26, 1997)".) Thanks, KJ Get your FREE Email at http://mailcity.lycos.com Get your PERSONALIZED START PAGE at http://personal.lycos.com