Modeling 1/f noise

TL;DR

This paper presents a simple analytical model demonstrating that 1/f noise can originate from the statistical distribution of transit times between pulses or particles, linking noise intensity to interval distributions.

Contribution

The study introduces a solvable model connecting 1/f noise to pulse transit time statistics, providing insights into its parameter dependencies and origins.

Findings

1/f noise arises from transit time statistics with random increments

Noise intensity relates to the distribution of time intervals

Clustering of pulses can produce 1/f noise

Abstract

The noise of signals or currents consisting from a sequence of pulses, elementary events or moving discrete objects (particles) is analyzed. A simple analytically solvable model is investigated in detail both analytically and numerically. It is shown that 1/f noise may result from the statistics of the pulses transit times with random increments of the time intervals between the pulses. The model also serves as a basis for revealing parameter dependences of 1/f noise and allows one to make some generalizations. As a result the intensity of 1/f noise is expressed through the distribution and characteristic functions of the time intervals between the subsequent transit times of the pulses. The conclusion that 1/f noise may result from the clustering of the signal pulses, elementary events or particles can be drawn from the analysis of the model systems.