I just neatened that up into an abstration + help All vanilla Replaced [abs~] More efficient [q8-sqrt~] seens fine No need for pi multiplier as is implicit in [cos~] radians (?) Martins histogram in separate GOP abs If I made a mistake please correct and repost. a. On Sun, 16 Mar 2008 21:13:04 +0000 Andy Farnell <[EMAIL PROTECTED]> 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 <[EMAIL PROTECTED]> 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 <[EMAIL PROTECTED]> 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 > > >>>>> <[EMAIL PROTECTED]> 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 > > >>>> > > >>>> > > >>>> ------------------------------------------------------------------------ > > >>>> > > >>>> _______________________________________________ > > >>>> PD-list@iem.at mailing list > > >>>> UNSUBSCRIBE and account-management -> > > >>>> http://lists.puredata.info/listinfo/pd-list > > >>> > > >>> ------------------------------------------------------------------------ > > >>> > > >>> _______________________________________________ > > >>> PD-list@iem.at mailing list > > >>> UNSUBSCRIBE and account-management -> > > >>> http://lists.puredata.info/listinfo/pd-list > > >> > > > > > > > > > > > > > -- > Use the source > > _______________________________________________ > PD-list@iem.at mailing list > UNSUBSCRIBE and account-management -> > http://lists.puredata.info/listinfo/pd-list -- Use the source
guassian-noise.tar.gz
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