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Student Support Forum: 'Problems with ciclicar convolution using FT' topicStudent Support Forum > General > "Problems with ciclicar convolution using FT"

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Filipe
09/14/08 3:23pm

I'm trying to use Mathematica to do a convolution of two gaussians with a rectangular function but I am getting very strange results.

Gaussian[x0_, \[Sigma]_] :=
1/((2 \[Pi])^(1/2) \[Sigma]) Exp[-((x - x0)^2/(2 \[Sigma]^2))]

\[Rho] = Gaussian[-1/2, \[Sigma]] +
Gaussian[1/2, \[Sigma]] /. \[Sigma] -> 1/10

F = FourierTransform[\[Rho], x, h]

In fourier terms we can do the same thing using a convolution with an averaging filter

Kernel = 1/PixelSize UnitStep[PixelSize/2 + h]
UnitStep[PixelSize/2 - h]

Filter = 2 (\[Pi]/2)^(1/2) InverseFourierTransform[Kernel, h, x]

Blurred = FullSimplify[InverseFourierTransform[F, h, x]*Filter]

The problem is here. The result of the fourier transform doesn't make any sense and it completely different of the non filtered \[Rho]
BlurredF = FourierTransform[Blurred, x, h]

The result is complitely different from the expected two blurred gaussians.

Where did I go wrong?

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Subject (listing for 'Problems with ciclicar convolution using FT')
Author Date Posted
Problems with ciclicar convolution using FT Filipe 09/14/08 3:23pm
Re: Problems with ciclicar convolution using FT Peter Pein 09/16/08 09:08am
Re: Re: Problems with ciclicar convolution usin... Filipe 09/16/08 3:23pm
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