[From Richard Kennaway (2007.01.15.1238 GMT)]
(Read parts 1 and 2 first.)
A graph of the resulting force against time showed it to be still too jaggedy for my purpose, so I repeated the smoothing process:
x(n) = new random value
y(n) = p x(n) + (1-p) y(n-1)
Y(n) = K1 y(n)
f(n) = p Y(n) + (1-p) f(n-1)
F(n) = K2 f(n)
One could repeat this again, but there's almost no difference in the visual appearance of the graphs of the twice-smoothed sequence and a three-times-smoothed sequence.
You can simultaneously generate any number of random variables in this way. The correlation between any two of them over a time interval will approach zero as the interval increases, with an exponential time constant of the order of t0.
-- Richard Kennaway