TY - JOUR
T1 - Exactly solvable model of continuous stationary 1/f noise
AU - Gleeson, James P.
PY - 2005/7
Y1 - 2005/7
N2 - An exactly solvable model generating a continuous random process with a 1/f power spectrum is presented. Examples of such processes include the angular (phase) speed of trajectories near stable equilibrium points in two-dimensional dynamical systems perturbed by colored Gaussian noise. An exact formula giving the correlation function of the 1/f noise in terms of the correlation of the perturbing colored noises is derived, and used to show that the 1/f spectrum is found in a wide variety of cases. The 1/f noise is non-Gaussian, as demonstrated by calculating its one-time probability distribution function. Numerical simulations confirm and extend the theoretical results.
AB - An exactly solvable model generating a continuous random process with a 1/f power spectrum is presented. Examples of such processes include the angular (phase) speed of trajectories near stable equilibrium points in two-dimensional dynamical systems perturbed by colored Gaussian noise. An exact formula giving the correlation function of the 1/f noise in terms of the correlation of the perturbing colored noises is derived, and used to show that the 1/f spectrum is found in a wide variety of cases. The 1/f noise is non-Gaussian, as demonstrated by calculating its one-time probability distribution function. Numerical simulations confirm and extend the theoretical results.
UR - http://www.scopus.com/inward/record.url?scp=27244450987&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.72.011106
DO - 10.1103/PhysRevE.72.011106
M3 - Article
AN - SCOPUS:27244450987
SN - 1539-3755
VL - 72
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 1
M1 - 011106
ER -