Exact numerical simulation of power-law noises

Abstract

Many simulations of stochastic processes require colored noises: I describe here an exact numerical method to simulate power-law noises: the method can be extended to more general colored noises, and is exact for all time steps, even when they are unevenly spaced (as may often happen for astronomical data, see e.g. N. R. Lomb, Astrophys. Space Sci. {\bf 39}, 447 (1976)). The algorithm has a well-behaved computational complexity, it produces a nearly perfect Gaussian noise, and its computational efficiency depends on the required degree of noise Gaussianity.

14 postscript figures, accepted for publication on Phys. Rev. E

References in corpus (3)

• Point process model of 1/f noise versus a sum of Lorentzians
• Fluctuations Do Matter: Large Noise-Enhanced Halos in Charged-Particle Beams
• Production of Enhanced Beam Halos via Collective Modes and Colored Noise

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• New version of PLNoise: a package for exact numerical simulation of power-law noises
• Artifacts with uneven sampling of red noise
• Long-range correlations with finite-size effects from a superposition of uncorrelated pulses with power-law distributed durations
• Scaling theory for the $1/f$ noise