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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



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