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Self-Organized Criticality by Henrik Jeldtoft Jensen

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D

Power Spectra and the Correlation Function

To get a feeling for the autocorrelation function G(τ) defined in (2.1), let us consider a signal that can assume only (and with equal probability) the two values F and − F. The signal switches at random from N(τ) = F to N(τ) = − F with a constant probability λ per time unit (MacDonald 1962). Thus, N(τ0)τ0 = 0. The autocorrelation function can be calculated according to the number of times the signal has managed to switch during the time interval τ:

(D.1)

The first line in this formula describes ...

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