scholarly journals Evaluation of the difference of pseudorandom signal from white noise using a parameter of energy spectrum model of the signal

2020 ◽  
Vol 24 (2) ◽  
Author(s):  
Z. A. Kolodiy ◽  
J. Z. Zvizlo
Keyword(s):  
Energy Spectrum ◽  
White Noise ◽  
The Difference ◽  
Spectrum Model ◽  
Pseudorandom Signal

Stress Induced Reordering in Amorphous Metals Analyzed by Relaxation Time and Activation Energy Spectrum Model

1995 ◽  
Vol 97-98 ◽  
pp. 97-102 ◽  
Author(s):  
Václav Ocelík ◽  
Kornel Csach ◽  
A. Kasardová ◽  
Jozef Miškuf ◽  
Vladimir Z. Bengus ◽  
...  
Keyword(s):  
Activation Energy ◽  
Relaxation Time ◽  
Energy Spectrum ◽  
Amorphous Metals ◽  
Spectrum Model

A Procedure for the Automatic Determination of Filter Cutoff Frequency for the Processing of Biomechanical Data

1999 ◽  
Vol 15 (3) ◽  
pp. 303-317 ◽  
Author(s):  
John H. Challis
Keyword(s):  
White Noise ◽  
Autocorrelation Function ◽  
Cutoff Frequency ◽  
Human Movement ◽  
Data Sets ◽  
Mathematical Functions ◽  
The Best Approximation ◽  
Second Derivatives ◽  
Low Pass ◽  
The Difference

This article presents and evaluates a new procedure that automatically determines the cutoff frequency for the low-pass filtering of biomechanical data. The cutoff frequency was estimated by exploiting the properties of the autocorrelation function of white noise. The new procedure systematically varies the cutoff frequency of a Butterworth filter until the signal representing the difference between the filtered and unfiltered data is the best approximation to white noise as assessed using the autocorrelation function. The procedure was evaluated using signals generated from mathematical functions. Noise was added to these signals so mat they approximated signals arising from me analysis of human movement. The optimal cutoff frequency was computed by finding the cutoff frequency that gave me smallest difference between the estimated and true signal values. The new procedure produced similar cutoff frequencies and root mean square differences to me optimal values, for me zeroth, first and second derivatives of the signals. On the data sets investigated, this new procedure performed very similarly to the generalized cross-validated quintic spline.

ENERGY SPECTRUM OF DISTURBANCE AT TURBULENT TRANSITION VIA ENERGY GRADIENT METHOD

2012 ◽  
Vol 19 ◽  
pp. 293-303 ◽  
Author(s):  
HUA-SHU DOU ◽  
BOO CHEONG KHOO
Keyword(s):  
Energy Spectrum ◽  
Flow Instability ◽  
Three Dimensional ◽  
Wave Number ◽  
Gradient Theory ◽  
Turbulent Transition ◽  
Energy Gradient Theory ◽  
Energy Gradient ◽  
The Difference ◽  
2D And 3D

The energy gradient theory for flow instability and turbulent transition was proposed in our previous work. The theoretical result obtained accords well with some experimental data for pipe and channel flows in the literature. In the present study, the energy gradient theory is extended to examine the effect of disturbance frequency on turbulent transition. Then, the energy spectrum of disturbance at the turbulent transition is obtained, which scales with the wave number by an exponent of –2. This scaling is near to the K41 law of –5/3 for the full developed isentropic homogenous turbulence. The difference for the two energy spectra may be due to the intermittency of turbulence at the transition state. The intermittence causes the distribution of the energy spectrum to take on a steeper gradient (tending to –2 from –5/3). Finally, the flow instability leading to turbulent transition can be classified as two-dimensional (2D) or three-dimensional (3D) in terms of the wave number and the Re. It is found that there is an optimum wave number which separates the 2D and 3D transitions and at which the disturbance energy at transition is minimum.

The mixing layer and its coherence examined from the point of view of two-dimensional turbulence

1988 ◽  
Vol 192 ◽  
pp. 511-534 ◽  
Author(s):  
Marcel Lesieur ◽  
Chantal Staquet ◽  
Pascal Le Roy ◽  
Pierre Comte
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
White Noise ◽  
Mixing Layer ◽  
Finite Size ◽  
Spanwise Direction ◽  
Computational Domain ◽  
Two Dimensional ◽  
Infinite Domain ◽  
Kinetic Energy Spectrum

A two-dimensional numerical large-eddy simulation of a temporal mixing layer submitted to a white-noise perturbation is performed. It is shown that the first pairing of vortices having the same sign is responsible for the formation of a continuous spatial longitudinal energy spectrum of slope between k−4 and k−3. After two successive pairings this spectral range extends to more than 1 decade. The vorticity thickness, averaged over several calculations differing by the initial white-noise realization, is shown to grow linearly, and eventually saturates. This saturation is associated with the finite size of the computational domain.We then examine the predictability of the mixing layer, considering the growth of decorrelation between pairs of flows differing slightly at the first roll-up. The inverse cascade of error through the kinetic energy spectrum is displayed. The error rate is shown to grow exponentially, and saturates together with the levelling-off of the vorticity thickness growth. Extrapolation of these results leads to the conclusion that, in an infinite domain, the two fields would become completely decorrelated. It turns out that the two-dimensional mixing layer is an example of flow that is unpredictable and possesses a broadband kinetic energy spectrum, though composed mainly of spatially coherent structures.It is finally shown how this two-dimensional predictability analysis can be associated with the growth of a particular spanwise perturbation developing on a Kelvin-Helmholtz billow: this is done in the framework of a one-mode spectral truncation in the spanwise direction. Within this analogy, the loss of two-dimensional predictability would correspond to a return to three-dimensionality and a loss of coherence. We indicate also how a new coherent structure could then be recreated, using an eddy-viscosity assumption and the linear instability of the mean inflexional shear.

scholarly journals Over-whitening or Pre-whitening in Hydro-climatological Trend Analysis?

2022 ◽  
Author(s):  
Zekai Sen
Keyword(s):  
Time Series ◽  
White Noise ◽  
Trend Analysis ◽  
Serial Correlation ◽  
Original Time Series ◽  
Trend Component ◽  
The Difference ◽  
Temperature Records ◽  
Original Time ◽  
Trend Identification

Abstract To meet the basic assumption of classical Mann-Kendall (MK) trend analysis, which requires serially independent time series, a pre-whitening (PW) procedure is proposed to alleviate the serial correlation structure of a given hydro-meteorological time series records for application. The procedure is simply to take the lagged differences in a given time series in the hope that the new time series will have an independent serial correlation coefficient. The whole idea was originally based on the first-order autoregressive AR (1) process, but such a procedure has been documented to damage the trend component in the original time series. On the other hand, the over-whitening procedure (OW) proposes a white noise process superposition of the same length with zero mean and some standard deviation on the original time series to convert it into serially independent series without any damage to the trend component. The stationary white noise addition does not have any trend components. For trend identification, annual average temperature records in New Jersey and Istanbul are presented to show the difference between PW and OW procedures. It turned out that the OW procedure was superior to the PW procedure, which did not cause a loss in the original trend component.

Aging of glassy transformer core alloys and the activation energy spectrum model

1993 ◽  
Vol 73 (10) ◽  
pp. 5366-5368 ◽  
Author(s):  
V. R. V. Ramanan ◽  
H. H. Liebermann
Keyword(s):  
Activation Energy ◽  
Energy Spectrum ◽  
Transformer Core ◽  
Spectrum Model

Analytical and Simulation Results for the Stochastic Spatial Fitzhugh-Nagumo Model Neuron

2008 ◽  
Vol 20 (12) ◽  
pp. 3003-3033 ◽  
Author(s):  
Henry C. Tuckwell
Keyword(s):  
White Noise ◽  
Model Neuron ◽  
Space Time ◽  
Noise Amplitude ◽  
Amplitude Noise ◽  
Analytical Results ◽  
Uniform Noise ◽  
Simulation Results ◽  
The Difference ◽  
Parameter Ranges

For the Fitzhugh-Nagumo system with space-time white noise, we use numerical methods to consider the generation of action potentials and the reliability of transmission in the presence of noise. The accuracy of simulated solutions is verified by comparison with known exact analytical results. Noise of small amplitude may prevent transmission directly, whereas larger-amplitude noise may also interfere by producing secondary nonlocal responses. The probability of transmission as a function of noise amplitude is found for both uniform noise and noise restricted to a patch. For certain parameter ranges, the recovery variable may be neglected to give a single-component nonlinear diffusion with space-time white noise. In this case, analytical results are obtained for small perturbations and noise, which agree well with simulation results. For the voltage variable, expressions are given for the mean, covariance, and variance and their steady-state forms. The spectral density of the voltage is also obtained. Numerical examples are given of the difference between the properties of nonlinear and linear cables, and the validity of the expressions obtained for the statistical properties is investigated as a function of noise amplitude. For given parameters, analytical results are in good agreement with simulation until a certain critical noise amplitude is reached, which can be estimated. The role of trigger zones in increasing the reliability of transmission is discussed.

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