Models for generation 1/f noise

TL;DR

This paper introduces simple, analytically solvable models that generate 1/f noise through fluctuating interevent times modeled as autoregressive processes, providing insights into the origin of 1/f noise.

Contribution

It presents new models that analytically produce 1/f noise, linking it to Brownian motion in interevent times, and explains its possible origins.

Findings

Models exhibit 1/f spectrum over wide frequency range

Power spectrum aligns with Hooge formula

Interevent time fluctuations cause 1/f noise

Abstract

Simple analytically solvable models are proposed exhibiting 1/f spectrum in wide range of frequency. The signals of the models consist of pulses (point process) which interevent times fluctuate about some average value, obeying an autoregressive process with very small damping. The power spectrum of the process can be expressed by the Hooge formula. The proposed models reveal possible origin of 1/f noise, i.e., random increments of the time intervals between pulses or interevent time of the process (Brownian motion in the time axis).