1/f noise: a pedagogical review

TL;DR

This pedagogical review comprehensively explains 1/f^ noise, covering its theoretical foundations, statistical properties, physical origins, and applications across various systems, highlighting its ubiquity and significance in science.

Contribution

It provides an accessible overview of 1/f^ noise, integrating theoretical, empirical, and computational perspectives to enhance understanding of its diverse manifestations.

Findings

1/f^ noise arises from superposition of relaxation processes

It exhibits infinite fluctuations at low frequencies

It appears in physical, biological, and geophysical systems

Abstract

This is a pedagogical review of the ubiquitous 1/f^\alpha noises. The sections include the representation of 1/f^\alpha noise as a superposition of many relaxation processes; a discussion of the infinitely large fluctuations in the low frequency limit; 1/f^\alpha noise from diffusion processes; the measured statistical properties of 1/f^\alpha noises; 1/f^\alpha noises in self organized criticality; scaling laws in earthquake physics; 1/f noise in deterministic dynamical systems; an example of noise in a biophysical system; the numerical simulation of 1/f^\alpha noise; 1/f noise literature (including online resources).