# 1/f noise

@article{Keshner19821fN, title={1/f noise}, author={M. 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… Expand

#### 819 Citations

Discrete-time simulation model for 1/f noise

- Physics
- IEEE 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… Expand

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

- Mathematics, Medicine
- Theoretical 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. Expand

Estimation of 1=f Processes

- 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… Expand

Cognitive emissions of 1/f noise.

- Psychology, Medicine
- Psychological 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. Expand

1/f Noise in the Computation Process by Rule 110

- Computer Science, Mathematics
- J. 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. Expand

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

- Engineering, Computer Science
- Proceedings 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. Expand

1/f Noise and Fractals in Economic Time Series

- Mathematics
- 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… Expand

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

- Mathematics, Computer Science
- IEEE 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. Expand

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

- Mathematics
- 2009

1/f noise and statistically self-similar random processes such as fractional Brownian motion (fBm) and fractional Gaussian noise (fGn) are fundamental models for a host of real-world phenomena, from… Expand

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

- Physics, Medicine
- Proceedings 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. Expand

#### References

SHOWING 1-10 OF 12 REFERENCES

Microcycle spectral estimates of 1/f noise in semiconductors

- Physics
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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… Expand

’’1/f noise’’ in music: Music from 1/f noise

- Physics
- 1978

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… Expand

1/f (Flicker) Noise: A Brief Review

- Computer Science
- 33rd 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. Expand

Some noises with I/f spectrum, a bridge between direct current and white noise

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- IEEE Trans. Inf. Theory
- 1967

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. Expand

Discussion of recent experiments on 1/ƒ noise

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Abstract The experimental evidence for the existence of bulk 1/ƒ noise is discussed. An empirical relation between the magnitude of the noise and the number of free charge carriers is given. The 1/ƒ… Expand

Fluctuation phenomena in nerve membrane

- Materials Science
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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… Expand

1/f noise

- Computer Science
- 1976

A survey is given of the recent literature on 1/ f noise and proposed models for mathematical models, empirical relations and physical models are discussed. Expand

LOW FREQUENCY NOISE IN TIN and LEAD FILMS AT THE SUPERCONDUCTING TRANSITION

- Materials Science
- 1976

We have measured the noise power spectra S/subV/(f) of tin and lead films at the superconducting transition in the frequency range 0.1 Hz to 5 kHz. Two types of samples were made: Type A were… Expand

Cyclic Changes in Insulin Needs of an Unstable Diabetic

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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. Expand

Some long‐run properties of geophysical records

- History
- 1969

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… Expand