[PD] Box Muller Gaussian noise

[Andy Farnell]

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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> > 
> 
> 


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