       Re: Convolution Integrals

• To: mathgroup at smc.vnet.net
• Subject: [mg16835] Re: Convolution Integrals
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Thu, 1 Apr 1999 21:35:16 -0500
• Organization: University of Western Australia
• References: <7dprk0\$dqc@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```The following code is fine:

<<Statistics`ContinuousDistributions`
<<Calculus`FourierTransform`
dist1=NormalDistribution[10,3];
pdf1=PDF[dist1,x];
dist2=NormalDistribution[5,4];
pdf2=PDF[dist2,x];
trans1=FourierTransform[pdf1,x,s];
trans2=FourierTransform[pdf2,x,s];

> I seem to be able to get to the inverse transform alright but how do I
> plot the final distribution?

To get the convolution (your syntax omitted s and x) you need

conv = InverseFourierTransform[trans1 trans2, s, x]

You can then Plot the pdf and convolution together:

Plot[{pdf1, pdf2, conv}, {x, -10, 30}, PlotRange -> All,
PlotStyle -> Table[Hue[i], {i, 0, 1, 1/3}]];

Cheers,
Paul

____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia
Nedlands WA  6907                     mailto:paul at physics.uwa.edu.au
AUSTRALIA                        http://www.physics.uwa.edu.au/~paul

God IS a weakly left-handed dice player
____________________________________________________________________

```

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