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White noise

About: White noise is a research topic. Over the lifetime, 16496 publications have been published within this topic receiving 318633 citations.


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TL;DR: In this paper, it was shown that the power spectra of these geophysical variables obey a scaling law, i.e., the power spectrum of a scaling variable is proportional to some power of the frequency, and that frequency-dependent noise models are more appropriate for modelling the spatial variation of geophysical parameters than the widely assumed white noise (frequency-independent) model.
Abstract: SUMMARY We have examined acoustic, density resistivity, gamma-ray and neutron logs from a number of boreholes in both sedimentary and igneous sequences. We show that the power spectra of these geophysical variables obey a scaling law, that is, the power spectra are proportional to some power of the frequency. In general, the power spectra are approximately inversely proportional to the frequency. This suggests that frequency-dependent noise models are more appropriate for modelling the spatial variation of geophysical parameters than the widely assumed white noise (frequency-independent) model and should be incorporated into the inversion for these variables, through a priori parameter covariances. the covariance of a scaling variable is simply obtained from the power spectrum. It is independent of the absolute value of the lag, that is, there is no preferred length scale, but is dependent upon the sample length. We demonstrate the advantage of scaling noise covariances with the inversion of DC resistivity sounding data both with the exact covariance and with the approximate case of inverse proportionality. Adoption of a frequency-dependent noise model leads to a reduction in the a posteriori parameter variances and to solutions exhibiting a degree of smoothness commensurate with measured spatial variations of these parameters.

70 citations

Journal ArticleDOI
TL;DR: This paper presents an approach to the design of linear DMAs that first transforms the microphone array signals into the short-time Fourier transform (STFT) domain and then converts the DMA beamforming design to simple linear systems to solve.
Abstract: Differential microphone array (DMA), a particular kind of sensor array that is responsive to the differential sound pressure field, has a broad range of applications in sound recording, noise reduction, signal separation, dereverberation, etc. Traditionally, an Nth-order DMA is formed by combining, in a linear manner, the outputs of a number of DMAs up to (including) the order of N − 1. This method, though simple and easy to implement, suffers from a number of drawbacks and practical limitations. This paper presents an approach to the design of linear DMAs. The proposed technique first transforms the microphone array signals into the short-time Fourier transform (STFT) domain and then converts the DMA beamforming design to simple linear systems to solve. It is shown that this approach is much more flexible as compared to the traditional methods in the design of different directivity patterns. Methods are also presented to deal with the white noise amplification problem that is considered to be the biggest hurdle for DMAs, particularly higher-order implementations.

70 citations

Journal ArticleDOI
TL;DR: In this article, the authors present a brief overview of the recent investigations aimed at understanding features of stochastic dynamics under the influence of Levy white noise perturbations, and find that the archetypal phenomena of noise-induced ordering are robust and can be detected also in systems driven by memoryless, non-Gaussian, heavy-tailed fluctuations with infinite variance.
Abstract: A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the existence of timescale separation between the dynamics of the measured observable and the typical timescale of the noise allows external fluctuations to be modeled as temporally uncorrelated and therefore white. However, in many natural phenomena the assumptions concerning the above mentioned properties of 'Gaussianity' and 'whiteness' of the noise can be violated. In this context, in contrast to the spatiotemporal coupling characterizing general forms of non-Markovian or semi-Markovian Levy walks, so called Levy flights correspond to the class of Markov processes which can still be interpreted as white, but distributed according to a more general, infinitely divisible, stable and non-Gaussian law. Levy noise-driven non-equilibrium systems are known to manifest interesting physical properties and have been addressed in various scenarios of physical transport exhibiting a superdiffusive behavior. Here we present a brief overview of our recent investigations aimed at understanding features of stochastic dynamics under the influence of Levy white noise perturbations. We find that the archetypal phenomena of noise-induced ordering are robust and can be detected also in systems driven by memoryless, non-Gaussian, heavy-tailed fluctuations with infinite variance.

70 citations

Journal ArticleDOI
30 Mar 2006-Chaos
TL;DR: It is analytically proved that chaos synchronization could be achieved with probability one merely via white-noise-based coupling and supports the observation of an interesting phenomenon that a certain kind of white noise could enhance chaos synchronization between two chaotic oscillators.
Abstract: In the paper, complete synchronization of two chaotic oscillators via unidirectional coupling determined by white noise distribution is investigated. It is analytically proved that chaos synchronization could be achieved with probability one merely via white-noise-based coupling. The established theoretical result supports the observation of an interesting phenomenon that a certain kind of white noise could enhance chaos synchronization between two chaotic oscillators. Furthermore, numerical examples are provided to illustrate some possible applications of the theoretical result.

70 citations

Journal ArticleDOI
TL;DR: In this article, a hierarchical entropy (HE) method was developed to quantify the complexity of a time series based on hierarchical decomposition and entropy analysis, which is applied to the Gaussian white noise and the 1/f noise.

70 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023238
2022535
2021488
2020541
2019558
2018537