[sdiy] different distributions from LFSR was: (oops) EN #76 question
gsn10 at hotmail.com
Wed Feb 6 23:35:52 CET 2013
There was previous discussion of summing multiple taps of an LFSR with different weights to obtain different distributions (normal and uniform), which was revisited in Electronotes 212. I did a little bit of messing around with this.
First, it should be obvious from the description of the uniform distributed case (sum different taps with binary weights) that this can be easily extended to an IIR filter with a feedback coefficient of either 0.5 or -0.5, with any delay length. So the noise source can have a uniform distribution with a lowpass, highpass or comb filtered response. I also tried it with an allpass filter. An allpass filter with a coefficient of +/- 0.5 (again with any delay length) results in a uniform distribution with smaller uniform "sidelobes" at half the probability. Different families of distributions can be created by varying the feedback coefficient.
Note that this only applies to binary sequences with good statistical properties. Arbitrary binary sequences will result in different distributions.
I know this is probably only of marginal interest, but I thought it was
sort of cool. I've already used it as a random note generator. I like that the distribution and correlation over time can
be varied somewhat independently. And maybe there are interesting
implications for some sort of chaotic feedback system...
I wrote an Octave script for it, if anyone wants to mess with it.
I also remember reading in composer Warren Burt's 1975 Master's thesis (describing the construction of the Aardvarks IV synthesizer with stochastic, time-variant timbre) that he used a similar circuit with binary weighted resistors. He used 16 sets of latches and resistor arrays to asynchronously sample a single LFSR. He didn't want the distributions to be identical for each of the 16 channels, so he imparted some Cageian variation to some of the resistor values by physically damaging them with a hammer. This was used for a sound installation in a grocery store. It was in the cheese department.
More on that here, near the bottom: http://www.warrenburt.com/my-history-with-music-tech2/
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