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From: e_meier@unibw-hamburg.de (Wilhelm Meier)
Subject: Re: White noise to gaussian noise
In-Reply-To: pilard@quartz.lmcp.jussieu.fr's message of 7 Dec 1994 12:09:08 GMT
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Date: Thu, 8 Dec 1994 06:30:35 GMT
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In article <3c48l4$sb5@vishnu.jussieu.fr> pilard@quartz.lmcp.jussieu.fr (Mathieu Pilard) writes:

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> From: pilard@quartz.lmcp.jussieu.fr (Mathieu Pilard)
> Newsgroups: sci.image.processing
> Date: 7 Dec 1994 12:09:08 GMT
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> How can i build a gaussian noise generator from a white noise generator??
> Help!!!
> Thank you
> Matthieu Pilard
> 

Probably you mean: how can I get gaussian distributed noise from 
UNIFORM distributed noise !


1) You can add some ARBITRARY distributed random variables and you get
   (due to the central limit theorem) a gaussian distribution. This works
   well for 10-20 samples you add to get one sample of the gaussian distribution.
   But its time consuming !

2) Let u1, u2 be two independent, uniform [0,1] distributed random variables.
   Then, with v1=2u1-1, v2=2u2-1 and s=v1^2 + v2^2

   x1 = v1 sqrt(-2 ln(s) / s)
   x2 = v2 sqrt(-2 ln(s) / s)
   
   are two (uncorrelated I guess) gaussian variables.

Hope that helps!
Wilhelm
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