Universal spectral densities: white and flicker noises. (21st August 2018)

• Record Type: Journal Article
• Authors: Eliazar, Iddo I; Sokolov, Igor M
• Is Part Of: Journal of physics. Volume 51:Number 38(2018)
• Publication Date: 2018-08-21
• Subjects: power spectra -- 1/f noise -- flicker noise -- random walks -- geometric random walks -- selfsimilar motions -- universality; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aad372
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: In this paper we introduce and analyze a model of a random collection of random oscillators. The model has a random number of oscillators, the oscillators have random amplitudes and random frequencies, and the model's output is the aggregate of its oscillators' outputs. Also, the model has two time scales: a 'human' time scale, over which the spectral density of the model's output is measured; and a 'cosmic' or a 'geological' time scale, over which the model's random parameters slowly evolve. Analyzing the model we establish that, with respect to the evolution of the oscillators' frequencies: (i) general random-walk dynamics universally yield white noise, i.e. flat spectral densities; (ii) general geometric random-walk dynamics universally yield 1/ f noise, i.e. harmonic spectral densities; and (iii) general Gaussian geometric random-walk dynamics universally yield white noise and flicker noise, i.e. inverse power-law spectral densities.