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
and 
is generated. The numbers are distributed binomially between 
and
, 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 
would also generate a white noise sequence,
this time between 
and 
and distributed with equal
probability over the six numbers
![$\displaystyle \left[-\frac{5}{2}, -\frac{3}{2}, -\frac{1}{2}, \frac{1}{2}, \frac{3}{2}, \frac{5}{2}\right].$](http://www.dsprelated.com/josimages_new/sasp2/img2686.png) |
(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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Independent Implies Uncorrelated
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Sample Power Spectral Density
