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Related Experiment Video

Updated: Jun 8, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Universal generation of 1/f noises.

Iddo Eliazar¹, Joseph Klafter

¹Department of Technology Management, Holon Institute of Technology, Israel. eliazar@post.tau.ac.il

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 28, 2010

Summary

This study reveals a universal mechanism for generating 1/f noise using a signal-superposition model. Randomizing transmission parameters of independent sources creates 1/f noise, akin to a randomized central limit theorem.

Area of Science:

Physics
Signal Processing
Complex Systems

Background:

1/f noise, also known as pink noise, is prevalent in various natural and artificial systems.
Existing models for 1/f noise generation are often system-specific and lack universality.
Understanding the fundamental mechanisms of 1/f noise is crucial for fields ranging from electronics to geophysics.

Purpose of the Study:

To establish a universal mechanism for the generation of 1/f noise.
To demonstrate that signal superposition from independent sources with randomized parameters can produce 1/f noise.
To explore the mathematical underpinnings of this noise generation process.

Main Methods:

Development of a signal-superposition model with independent sources.

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Introduction of random transmission parameters (amplitude, frequency, initiation epoch) for each source.

Mathematical analysis of the power spectrum of the superimposed signal under parameter randomization.

Main Results:

The proposed model successfully generates 1/f noise.
Randomization of transmission parameters renders the power spectrum invariant to the specific stochastic signal pattern.
The findings are analogous to a randomized central limit theorem for 1/f noise.

Conclusions:

A universal mechanism for 1/f noise generation has been established through signal superposition.
The study provides a foundational understanding of 1/f noise across diverse applications.
This work offers a new perspective on noise generation through a randomized central limit theorem approach.