1 research outputs found
Point process model of 1/f noise versus a sum of Lorentzians
We present a simple point process model of noise, covering
different values of the exponent . The signal of the model consists of
pulses or events. The interpulse, interevent, interarrival, recurrence or
waiting times of the signal are described by the general Langevin equation with
the multiplicative noise and stochastically diffuse in some interval resulting
in the power-law distribution. Our model is free from the requirement of a wide
distribution of relaxation times and from the power-law forms of the pulses. It
contains only one relaxation rate and yields spectra in a wide
range of frequency. We obtain explicit expressions for the power spectra and
present numerical illustrations of the model. Further we analyze the relation
of the point process model of noise with the Bernamont-Surdin-McWhorter
model, representing the signals as a sum of the uncorrelated components. We
show that the point process model is complementary to the model based on the
sum of signals with a wide-range distribution of the relaxation times. In
contrast to the Gaussian distribution of the signal intensity of the sum of the
uncorrelated components, the point process exhibits asymptotically a power-law
distribution of the signal intensity. The developed multiplicative point
process model of noise may be used for modeling and analysis of
stochastic processes in different systems with the power-law distribution of
the intensity of pulsing signals.Comment: 23 pages, 10 figures, to be published in Phys. Rev.