# 1/f noise

@article{Keshner19821fN, title={1/f noise}, author={Marvin S. Keshner}, journal={Proceedings of the IEEE}, year={1982}, volume={70}, pages={212-218} }

1/f noise is a nonstationary random process suitable for modeling evolutionary or developmental systems. It combines the strong influence of past events on the future and, hence somewhat predictable behavior, with the influence of random events. Nonstationary autocorrelation functions for 1/f noise are developed to demonstrate that its present behavior is equally correlated with both the recent and distant past. The minimum amount of memory for a system that exhibits 1/f noise is shown to be…

## 887 Citations

### Discrete-time simulation model for 1/f noise

- MathematicsIEEE Transactions on Electron Devices
- 2004

This paper proposes a simulation model based on the fact that 1/f processes belong to the class of statistically self-similar random processes. Unlike most of the earlier modeling approaches, which…

### Extinction risk and the 1/f family of noise models.

- PhysicsTheoretical population biology
- 1999

Predictions, based on explicit formulae and on simulations, indicate that for very short projection times relative to T, brown and pink noise models are usually optimistic relative to equivalent white noise model, and for projection timescales equal to and substantially greater than T, an equivalent brown or pink noise model usually predicts a greater extinction risk, unless CV is very large.

### Cognitive emissions of 1/f noise.

- PsychologyPsychological review
- 2001

This article shows that residual fluctuations that naturally arise in experimental inquiry may harbor a long-term memory process known as 1/f noise, which appears to be associated with the most elementary aspect of cognitive process, the formation of representations.

### Estimation of 1=f Processes

- Mathematics
- 2007

| It is well known that the time series behaviour of non-linear systems with fractal attractors has a hyperbolic (or 1=f) sample power spectral density. Recently there has been a lot of interest in…

### 1/f Noise in the Computation Process by Rule 110

- PhysicsJ. Cell. Autom.
- 2016

The power spectra of the computation process of rule 110 emulating cyclic tag system are investigated to suggest a possibility that the dynamics accompanied with 1/ f noise and the one capable of performing computation overlap each other in cellular automaton rule space.

### 1/f noise modeling using discrete-time self-similar systems

- PhysicsProceedings of the 2003 International Symposium on Circuits and Systems, 2003. ISCAS '03.
- 2003

A model based on the fact that 1/f processes belong to the class of statistically self-similar random processes is proposed, which generates 1/ f noise in the time domain with a simple white noise input and is parameterized by a quantity whose value can be adjusted to reflect the desired1/f parameter.

### 1/f Noise and Fractals in Economic Time Series

- Economics
- 1992

Many economic time series such as stock prices $ (t) have spectral densities S$ (f) thatp ] vary as I/f 2 and increments Δ$(t) with SΔ$(f) α constant, indicating they closely follow the efficient…

### A class of second-order stationary self-similar processes for 1/f phenomena

- Mathematics, Computer ScienceIEEE Trans. Signal Process.
- 1997

This study proposes a class of statistically self-similar processes and outlines an alternative mathematical framework for the modeling and analysis of 1/f phenomena based on the extensions of the basic concepts of classical time series analysis on the notion of stationarity.

### Fast, Exact Synthesis of Gaussian and nonGaussian Long-Range-Dependent Processes

- Computer Science
- 2009

This work develops a simple, fast, fast framework for exactly synthesizing a range of Gaussian and nonGaussian LRD processes and introduces and study a new bi-scaling fBm process featuring a “kinked” correlation function that exhibits distinct scaling laws at coarse and fine scales.

### A unified and universal explanation for Lévy laws and 1/f noises

- PhysicsProceedings of the National Academy of Sciences
- 2009

The classes of universal stationary laws and power spectra are shown to coincide, respectively, with the classes of Lévy laws and 1/f noises, providing a unified and universal explanation for the ubiquity of these classes of “anomalous statistics” in various fields of science and engineering.

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Many physical occurrences are characterized by extremely low spectral variations, the measurement and estimation of which has been invariably difficult. An estimate of the density of the power…

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The spectral density of fluctuations in the audio power of many musical selections and of English speech varies approximately as 1/f (f is the frequency) down to a frequency of 5×10−4 Hz. This result…

### 1/f (Flicker) Noise: A Brief Review

- Geology33rd Annual Symposium on Frequency Control
- 1979

In this paper a review is given of the systems exhibiting I / f noise and the postulates researchers have made about its origin.

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The present paper reinterprets spectral measurements without paradox, by introducing a concept to be called "conditional spectrum," and examples are given of functions ruled by chance, that have the observed "erratic" behavior and conditional spectral density.

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The fluctuations of the voltage across the resting membrane of myelinated nerve fibers have been analyzed. They show a 1/f spectrum and a Gaussian amplitude distribution and are related to the net…

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The fluctuating insulin requirements of an unstable diabetic over an 8-year period have been subjected to spectral analysis and the periodicities indicate that social causes play no major role but suggest that a weathermediated effect may exist.

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By preparing this book Chris Barton and Paul La Pointe have earned the gratitude of all geologists and students of fractals. I continue to belong to this second group, and Chris and Paul clearly have…