correlations and integrators (part 3)

[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