[PD] Box Muller Gaussian noise
Uğur Güney
ugurguney at gmail.com
Sun Mar 16 23:17:27 CET 2008
# Hi, sorry for jumping into the conversation. I am doing my
statistical physics homework and can not read whole mails just skim
read them and saw terms like "uniform distribution" and "gaussian
distribution". I thought it could be worth to mention the "central
limit theorem" which says that the cumulative effect of every kind of
distribution will become a gaussian distribution:
http://en.wikipedia.org/wiki/Illustration_of_the_central_limit_theorem
http://en.wikipedia.org/wiki/Central_limit_theorem
-ugur guney-
On Sun, Mar 16, 2008 at 11:13 PM, Andy Farnell
<padawan12 at obiwannabe.co.uk> wrote:
>
> Wow, that's a gorgeous demonstraton Martin!
>
> Everything becomes clear as time -> infinity :)
>
> And somehow our little Earthling brains are able to
> spot this signature distribution as we listen to rainfall.
>
> Now I'm getting how uniform fall leads to
> a Gaussian bell around the mean for an area over time.
>
> Thanks.
>
>
> Chuck, I'm sorry I couldn't follow all of your derivation
> of Box Muller, but thanks for the analysis. I think we agree
> it's a neat trick for an efficient source of WGN.
>
> thanks all,
>
> Andy
>
>
> On Sun, 16 Mar 2008 16:54:29 -0400
>
>
> Martin Peach <martin.peach at sympatico.ca> wrote:
>
> > Here's a histogram generator (binner) that shows the distribution of
> > [gaussianoise]. Using it I can quickly see that [gaussianoise2] is too
> > peaked around zero and that [gaussianoise3] chops the tails off when the
> > scale is low.
> > If you have uniformly distributed raindrops falling, any given area will
> > receive a number of raindrops that clusters about the mean in a normal
> > distribution, just as if you first bin the number of occurrences of each
> > value of white noise, then bin the resulting counts, the histogram of
> > the counts will look like a bell curve centered at the mean count.
> >
> > Martin
> >
> > Andy Farnell wrote:
> > >
> > > GEM is broken here, but thanks for the info Marius.
> > > I'm reading through the docs for R at the moment.
> > > It makes lovely plots, but haven't figured how to get
> > > my data in to it yet...
> > >
> > > JFYI the application is rainfall. Many papers I read describe
> > > rainfall as Gaussian.
> > >
> > > I know from physical analysis that raindrops are uniform in size
> > > and velocity for any local sample, so I've realised this distribution
> > > is about how they fall within an area and pondering how a
> > > distribution can be Gaussian in 2D.
> > >
> > > Thing is, I can't figure out any good reason why rain should
> > > by anything other than uniformly distributed ! :(
> > >
> > > When I use Martins second patch with a thresholding function
> > > to trigger droplet sounds, it does sound a lot more like
> > > real rainfall than a uniformly triggered model.
> > >
> > > I'm in one of those grey areas where I half understand what I'm
> > > doing, which is a dangerous place to be.
> > >
> > > Anybody know of cool papers I might have missed on the
> > > distribution of rain drops and the effect on their sound?
> > >
> > > Thanks,
> > >
> > > Andy
> > >
> > >
> > >
> > >
> > > On Sun, 16 Mar 2008 15:43:34 -0400
> > > marius schebella <marius.schebella at gmail.com> wrote:
> > >
> > >> from the first equation that andy posted, I produced a gem
> > >> representation. the box muller noise seems wrong, because it does not
> > >> use the whole range but is shifted to the negative side.
> > >> note, this is not a distribution of frequencies, but of noise values..
> > >> marius.
> > >>
> > >> Martin Peach wrote:
> > >>> Oh no that's wrong isn't it :(
> > >>> The log is necessary to keep the distribution normal, and the range is
> > >>> going to get wider the closer to zero the radius is allowed to get.
> > >>> The attached patch has a scale adjustment...
> > >>> Still I wonder what kind of distribution gaussianoise2 gives, it's not
> > >>> just white.
> > >>>
> > >>> Martin
> > >>>
> > >>>
> > >>> Martin Peach wrote:
> > >>>> Charles Henry wrote:
> > >>>>> On Sun, Mar 16, 2008 at 11:16 AM, Martin Peach
> > >>>>> <martin.peach at sympatico.ca> wrote:
> > >>>>>> (gaussianoise has occasional values that exceed [-1 ... 1], which I
> > >>>>>> suppose is normal...white noise is always on [-1...1])
> > >>>>> That's true. With the Box-Muller method, there is the log(~U1) term,
> > >>>>> but you can always just add a small value to U1, which will truncate
> > >>>>> your distribution. The size of the small value can be calculated to
> > >>>>> fit with any given threshold.
> > >>>>>
> > >>>> I think it's really because the Box-Muller method selects random
> > >>>> numbers in pairs which map to points in a unit square on the plane,
> > >>>> but then selects only those points which are inside the unit circle,
> > >>>> something that the pd patch doesn't do (how to resample points in a
> > >>>> dsp vector until they are in range?). The attached patch shows the
> > >>>> straightforward way of doing it by simply selecting a random radius
> > >>>> and angle and returning the resulting y coordinate as the random
> > >>>> number. The results are always on [-1,1].
> > >>>> I don't think sin~ will be any slower than log~.
> > >>>>
> > >>>> Martin
> > >>>>
> > >>>>
> > >>>> ------------------------------------------------------------------------
> > >>>>
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> > >
> >
> >
>
>
> --
> Use the source
>
>
>
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