On the estimation of spectra from randomly sampled signals: a method of reducing variability

1980 ◽  
Vol 371 (1745) ◽  
pp. 235-258 ◽  
Keyword(s):  
Numerical Experiments ◽  
Simulated Data ◽  
Spectral Energy ◽  
Mean Square ◽  
Sampled Data ◽  
Spectral Estimates ◽  
The Mean ◽  
The Stability ◽  
Analytical Expressions

Spectral estimates obtained from randomly sampled data arrays incur excess variability over and above that arising from the stochastic character of the signal. In previous papers estimators have been derived for both the direct transform and the correlation plane methods. Expressions for the excess variability showed its dependence on the magnitude of the mean square of the data. Here we show how improved estimates can be obtained by filtering out parts of the spectral energy so that the actual analysis for other parts of the spectrum can be performed on data of smaller mean square. The variability associated with this filtering operation limits the improvement in the stability of estimates that can be achieved. Analytical expressions for the bias and variability of these new estimates are compared with numerical experiments on simulated data arrays.

Stability Criteria for Distributed Nonlinear Sampled-Data Systems Defined by Green’s Functions

1974 ◽  
Vol 96 (3) ◽  
pp. 315-321 ◽  
Author(s):  
G. Jumarie
Keyword(s):  
Stability Criterion ◽  
Feedback Gain ◽  
Continuous Systems ◽  
Mean Square ◽  
Data Systems ◽  
Sampled Data ◽  
Input Output ◽  
Output Stability ◽  
Lumped Parameter ◽  
The Mean

Sampled-data, nonlinear, distributed systems, which exhibit a structure similar to that of the standard closed loop with lumped parameter, are investigated from the viewpoint of their input-output stability. These systems are governed by operational equations involving discrete Laplace-Green kernels. Their feedback gains are bounded by upper and lower values which depend explicitly on the time and the distributed parameter. The main result is: an input-output stability theorem is given which applies both in L∞ (O, ∞) and L2 (O, ∞). This criterion, which may be considered as being an extension of the ≪circle criterion≫, involves the mean square value on the bounds of the feedback gain. Stability conditions for continuous systems are derived from this result. In the special case of systems with distributed periodical time-varying feedback gains, a stability criterion is given which applies in Marcinkiewicz space M2 (O, ∞). This result which involves the mean square value of the feedback gain is generally less restrictive than the L2 (O, ∞) stability criterion mentioned above.

Acoustic Information Acquisition and Time Domain Analysis on Alternating Current Rail Flash Butt Welding

2012 ◽  
Vol 239-240 ◽  
pp. 16-20
Author(s):  
Qi Bing Lv ◽  
Ke Li Tan ◽  
Xi Zhang ◽  
Jian Chen ◽  
Guo Qing Liu
Keyword(s):  
Time Domain ◽  
Acoustic Signal ◽  
Information Acquisition ◽  
Welding Process ◽  
Welding Current ◽  
Time Domain Analysis ◽  
Mean Square ◽  
Butt Welding ◽  
The Mean ◽  
The Stability

Based on the mobile rail flash butt welding machine UN5-150ZB, the synchronous data acquisition hardware system was designed to collect welding current, welding voltage and flash acoustic signal in welding process, and the software platform with the functions of signal collecting, waveform display and data operation was developed by higher-level programming language LabVIEW. After the welding current, welding voltage and flash acoustic signal in welding process had been collected, the mean, variance and mean square value of flash acoustic signal in time-domain were analyzed. Through comparison, the relationship between these characteristics and the stability of flash was analyzed. The result shows that the changes of mean and variance of flash acoustic signal are not obvious, and do not correlate with stability of flash, but the mean square value in time domain is closely associated with the stability of flash, and the stability of flash can be indicated by the mean square value.

Strong Convergence Analysis of Split-Step θ-Scheme for Nonlinear Stochastic Differential Equations with Jumps

2016 ◽  
Vol 8 (6) ◽  
pp. 1004-1022 ◽  
Author(s):  
Xu Yang ◽  
Weidong Zhao
Keyword(s):  
Differential Equations ◽  
Theoretical Result ◽  
Strong Convergence ◽  
Stochastic Differential Equations ◽  
Rate Of Convergence ◽  
Numerical Experiments ◽  
Mean Square ◽  
Nonlinear Stochastic Differential Equations ◽  
Mean Square Convergence ◽  
The Mean

AbstractIn this paper, we investigate the mean-square convergence of the split-step θ-scheme for nonlinear stochastic differential equations with jumps. Under some standard assumptions, we rigorously prove that the strong rate of convergence of the split-step θ-scheme in strong sense is one half. Some numerical experiments are carried out to assert our theoretical result.

Frequency resolution of Fourier and maximum entropy spectral estimates

Geophysics ◽  
1982 ◽  
Vol 47 (9) ◽  
pp. 1303-1307 ◽  
Author(s):  
S. L. Marple
Keyword(s):  
Maximum Entropy ◽  
Signal To Noise Ratio ◽  
Frequency Resolution ◽  
Sampled Data ◽  
Signal To Noise ◽  
Analytic Determination ◽  
Spectral Estimates ◽  
The Mean ◽  
Better Than

An analytic determination of the frequency resolution for maximum entropy and conventional Blackman‐Tukey spectral estimates is made for the case of known autocorrelation. As the signal‐to‐noise ratio decreases, the maximum entropy resolution is no better than that achievable by the Blackman‐Tukey spectral estimate. The mean resolution of an ensemble of spectra constructed from sampled data sequences agrees with the analytic result.

Material’s Chemical Reaction Progression Variables Fluctuating and Detailed Equilibrium Principle

2012 ◽  
Vol 424-425 ◽  
pp. 861-864
Author(s):  
Qing Hua Zou
Keyword(s):  
Chemical Reaction ◽  
Equilibrium Equation ◽  
Internal Variable ◽  
Local System ◽  
Mean Square ◽  
Mean Square Deviation ◽  
Variable Chemical ◽  
The Mean ◽  
The Stability ◽  
Non Equilibrium

The paper derived and gave the mean square deviation formula relating to the internal variable (chemical reaction progression variable) fluctuating of the linear non–equilibrium local system, and also rendered the condition of the stability. Furthermore, It discussed the related relations among the corresponding mean square deviation, the detailed equilibrium equation, the relax time and other thermal mechanics variables

scholarly journals Strong solutions for the stochastic 3D LANS-α model driven by non-Gaussian Lévy noise

2015 ◽  
Vol 15 (02) ◽  
pp. 1550011
Author(s):  
Gabriel Deugoué ◽  
Mamadou Sango
Keyword(s):  
Strong Solution ◽  
Strong Solutions ◽  
Lévy Noise ◽  
Mean Square ◽  
Stability Of Solutions ◽  
Model Driven ◽  
The Mean ◽  
The Stability ◽  
Non Gaussian ◽  
Levy Noise

We establish the existence, uniqueness and approximation of the strong solutions for the stochastic 3D LANS-α model driven by a non-Gaussian Lévy noise. Moreover, we also study the stability of solutions. In particular, we prove that under some conditions on the forcing terms, the strong solution converges exponentially in the mean square and almost surely exponentially to the stationary solution.

The exponential behavior and stabilizability of quasilinear parabolic stochastic partial differential equation

2021 ◽  
pp. 1-13
Author(s):  
Xiuwei Yin ◽  
Guangjun Shen ◽  
Jiang-Lun Wu
Keyword(s):  
Exponential Stability ◽  
Mean Square ◽  
Exponential Behavior ◽  
Partial Differential ◽  
Stochastic Perturbations ◽  
Mean Square Stability ◽  
The Mean ◽  
The Stability ◽  
Exponential Mean Square Stability ◽  
Quasilinear Parabolic

In this paper, we study the stability of quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone. The exponential mean square stability and pathwise exponential stability of the solutions are established. Moreover, under certain hypothesis on the stochastic perturbations, pathwise exponential stability can be derived, without utilizing the mean square stability.

HAUSDORFF DIMENSION OF CONTINUOUS POLYAKOV’S RANDOM SURFACES

1990 ◽  
Vol 05 (06) ◽  
pp. 1093-1121 ◽  
Author(s):  
JACQUES DISTLER ◽  
ZVONIMIR HLOUSEK ◽  
HIKARU KAWAI
Keyword(s):  
Phase Transition ◽  
Hausdorff Dimension ◽  
Numerical Experiments ◽  
Discrete Models ◽  
Liouville Theory ◽  
Behavior Changes ◽  
Mean Square ◽  
Random Surfaces ◽  
Scaling Properties ◽  
The Mean

In this paper we compute exactly, using the scaling properties of the Liouville theory, the Hausdorff dimension of the continuous random surfaces of Polyakov for D≤1. We find that for D<1, the mean square size of the surface grows as a logarithm of the area of the surface as well as the area of the surface raised to a power, the power being minus the string susceptibility. For D=1 the behavior changes, as expected, because the model undergoes a phase transition. In that case we find that the mean square size of the surface behaves as a combination of terms that grow as a logarithm of the area as well as its square, in qualitative agreement with the results of numerical experiments in discrete models.

scholarly journals Thermodynamic properties of semiconductor compounds studied based on Debye-Waller factors

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Nguyen Van Hung ◽  
Nguyen Cong Toan ◽  
Nguyen Ba Duc ◽  
Dinh Quoc Vuong
Keyword(s):  
Thermodynamic Properties ◽  
Mean Square Displacement ◽  
Close Relation ◽  
Relative Displacement ◽  
Mean Square ◽  
Many Body ◽  
Zinc Blende ◽  
Semiconductor Compounds ◽  
The Mean ◽  
Analytical Expressions

AbstractThermodynamic properties of semiconductor compounds have been studied based on Debye-Waller factors (DWFs) described by the mean square displacement (MSD) which has close relation with the mean square relative displacement (MSRD). Their analytical expressions have been derived based on the statistical moment method (SMM) and the empirical many-body Stillinger-Weber potentials. Numerical results for the MSDs of GaAs, GaP, InP, InSb, which have zinc-blende structure, are found to be in reasonable agreement with experiment and other theories. This paper shows that an elements value for MSD is dependent on the binary semiconductor compound within which it resides.

scholarly journals The StochasticΘ-Method for Nonlinear Stochastic Volterra Integro-Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Peng Hu ◽  
Chengming Huang
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Numerical Experiments ◽  
Sufficient Condition ◽  
Asymptotically Stable ◽  
Mean Square ◽  
True Solution ◽  
Mean Square Exponential Stability ◽  
Mean Square Convergence ◽  
The Mean

The stochasticΘ-method is extended to solve nonlinear stochastic Volterra integro-differential equations. The mean-square convergence and asymptotic stability of the method are studied. First, we prove that the stochasticΘ-method is convergent of order1/2in mean-square sense for such equations. Then, a sufficient condition for mean-square exponential stability of the true solution is given. Under this condition, it is shown that the stochasticΘ-method is mean-square asymptotically stable for every stepsize if1/2≤θ≤1and when0≤θ<1/2, the stochasticΘ-method is mean-square asymptotically stable for some small stepsizes. Finally, we validate our conclusions by numerical experiments.

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