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Making White Noise with Dice

An example of a digital white noise generator is the sum of a pair of dice minus 7. We must subtract 7 from the sum to make it zero mean. (A nonzero mean can be regarded as a deterministic component at dc, and is thus excluded from any pure noise signal for our purposes.) For each roll of the dice, a number between $ 1+1-7 = -5$ and $ 6+6-7=5$ is generated. The numbers are distributed binomially between $ -5$ and $ 5$ , but this has nothing to do with the whiteness of the number sequence generated by successive rolls of the dice. The value of a single die minus $ 3.5$ would also generate a white noise sequence, this time between $ -2.5$ and $ +2.5$ and distributed with equal probability over the six numbers

$\displaystyle \left[-\frac{5}{2}, -\frac{3}{2}, -\frac{1}{2}, \frac{1}{2}, \frac{3}{2}, \frac{5}{2}\right].$ (C.27)

To obtain a white noise sequence, all that matters is that the dice are sufficiently well shaken between rolls so that successive rolls produce independent random numbers.C.4

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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University