A simple test of the Gaussian character of noise

Yakimov, A. V.; Hooge, F.N.

doi:10.1016/s0921-4526(99)01390-3

Cited by 28 publications

(10 citation statements)

References 5 publications

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“…This power law behavior 1/f α often persists over several orders of magnitude with cutoffs present at both high and low frequencies, and with typical values of α in the range 0.8 ≤ α ≤ 4 [2]. In a somewhat loose terminology, all these systems are said to display 1/f noise although good quality data with α very close to 1 exist only for the voltage fluctuations when a current is flowing through a resistor [3,4]. Phenomena with α = 1, however, are abundant, examples being the white-dwarf light emission [5], the flow of sand through hourglass [6], ionic current fluctuations in membrane channels [7], number of daily trades in the stock market [8], water flows of rivers [9], the spike trains of nerve cells [10], the occurrence of earthquakes [11], the traffic flow on a highway [12,13], the electric noise in carbon nanotubes [14] and in nanoparticle films [15], the interface fluctuations [16], dissipation in turbulent systems [17], and the list could be continued.…”

Section: Introductionmentioning

confidence: 99%

Roughness distributions for1/fαsignals

et al. 2002

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The probability density function (PDF) of the roughness, i.e., of the temporal variance, of 1/f α noise signals is studied. Our starting point is the generalization of the model of Gaussian, timeperiodic, 1/f noise, discussed in our recent Letter [1], to arbitrary power law. We investigate three main scaling regions (α ≤ 1/2, 1/2 < α ≤ 1, and 1 < α), distinguished by the scaling of the cumulants in terms of the microscopic scale and the total length of the period. Various analytical representations of the PDF allow for a precise numerical evaluation of the scaling function of the PDF for any α. A simulation of the periodic process makes it possible to study also non-periodic, thus experimentally more relevant, signals on relatively short intervals embedded in the full period. We find that for α ≤ 1/2 the scaled PDF-s in both the periodic and the non-periodic cases are Gaussian, but for α > 1/2 they differ from the Gaussian and from each other. Both deviations increase with growing α. That conclusion, based on numerics, is reinforced by analytic results for α = 2 and α → ∞, in the latter limit the scaling function of the PDF being finite for periodic signals, but developing a singularity for the aperiodic ones. Finally, an overview is given for the scaling of cumulants of the roughness and the various scaling regions in arbitrary dimensions. We suggest that our theoretical and numerical results open a new perspective on the data analysis of 1/f α processes.

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Section: Introductionmentioning

confidence: 99%

Roughness distributions for1/fαsignals

et al. 2002

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“…Yakimov and F.N. Hooge [26]. They considered n-type epitaxial GaAs films grown by molecular beam epitaxy.…”

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confidence: 99%

“…A noise-free current passed longitudinally through the film and other contacts were used as voltage probes both for longitudinal and transverse directions. Several time series with typically 163840 points were obtained and the power spectrum was found to exhibit 1/f behavior roughly over two decades [26] of frequencies. We have reanalyzed these data by dividing the signal into segments of length N = 32, 64, 128, 256, and computing the distributions of the roughness for different N .…”

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confidence: 99%

1/fNoise and Extreme Value Statistics

et al. 2001

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“…Usually, it is assumed that the observed noise is a Gaussian linear stochastic process, which implies that the power spectral density characterizes completely its statistical properties. However, non-Gaussian and nonlinear stochastic processes are present and play an important role in various semiconductor devices 6,7 . For example, in a presence of random telegraph noise, the observed deviation from a Gaussian distribution is used as a reliability prediction of semiconductor devices 8 .…”

Section: Measures Of Nonlinearitymentioning

confidence: 99%

Application of nonlinearity measures to chemical sensor signals

2003

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The stochastic component of chemical sensor signal contains valuable information that can be visualized not only by spectral analysis but also by using nonlinear characteristic components. The analysis of nonlinear stochastic components enables the extraction of physically interesting and useful features and may lead to significant improvements in selectivity and sensitivity. Various measures of nonlinearity are presented and estimated for sample sensor data obtained from commercial chemical sensors. Particular attention was paid to the bispectrum function that detects nonlinear and non-stationary components in the analyzed noise. The results suggest that bispectrum measurements provide valuable information about the nature of noise generation in chemical sensors. Moreover, we have found, by analyzing skewness and kurtosis distributions, that the measured time series were stationary.

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A simple test of the Gaussian character of noise

Cited by 28 publications

References 5 publications

Roughness distributions for1/fαsignals

Roughness distributions for1/fαsignals

1/fNoise and Extreme Value Statistics

Application of nonlinearity measures to chemical sensor signals

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