Analytical Fitting Functions of Finite Sample Discrete Entropies of White Gaussian Noise

In order to find the convergence rate of finite sample discrete entropies of a white Gaussian noise(WGN), Brown entropy algorithm is numerically tested.With the increase of sample size, the curves of these finite sample discrete entropies are asymptotically close to their theoretical values.The confidence intervals of the sample Brown entropy are narrower than those of the sample discrete entropy calculated from its differential entropy, which is valid only in the case of a small sample size of WGN. The differences between sample Brown entropies and their theoretical values are fitted by two rational functions exactly, and the revised Brown entropies are more efficient. The application to the prediction of wind speed indicates that the variances of resampled time series increase almost exponentially with the increase of resampling period.

GAUSSIAN WHITE NOISE CALCULUS OF GENERALIZED EXPANSION

A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators partial derivative(t) and its dual, creation operators partial derivative(t)*.

Stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise

The current paper is devoted to the study of the stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise. First, the dynamics of stochastic FitzHugh-Nagumo systems are studied. Then, the existence and uniqueness of their invariant measures, which mix exponentially are proved. Finally, the asymptotic behaviors of invariant measures when size of noise gets to zero are investigated.

Some Applications of Higher Moments of the Linear Gaussian White Noise Process

The Linear Gaussian white noise process is an independent and identically distributed (iid) sequence with zero mean and finite variance with distribution N (0, σ2 ) . Hence, if X1, x2, …, Xn is a realization of such an iid sequence, this paper studies in detail the covariance structure of X1d, X2d, …, Xnd, d=1, 2, …. By this study, it is shown that: 1) all powers of a Linear Gaussian White Noise Process are iid but, not normally distributed and 2) the higher moments (variance and kurtosis) of Xtd, d=2, 3, … can be used to distinguish between the Linear Gaussian white noise process and other processes with similar covariance structure.

Global Pressure of One-Dimensional Polydisperse Granular Gases Driven by Gaussian White Noise

We study the global pressure of a one-dimensional polydisperse granular gases system for the first time, in which the size distribution of particles has the fractal characteristic and the inhomogeneity is described by a fractal dimension D. The particles are driven by Gaussian white noise and subject to inelastic mutual collisions. We define the global pressure P of the system as the impulse transferred across a surface in a unit of time, which has two contributions, one from the translational motion of particles and the other from the collisions. Explicit expression for the global pressure in the steady state is derived. By molecular dynamics simulations, we investigate how the inelasticity of collisions and the inhomogeneity of the particles influence the global pressure. The simulation results indicate that the restitution coefficient e and the fractal dimension D have significant effect on the pressure.

Characteristic Analysis of White Gaussian Noise in S-Transformation Domain

The characteristic property of white Gaussian noise (WGN) is derived in S-transformation domain. The results show that the distribution of normalized S-spectrum of WGN follows X2?distribution with two degrees of freedom. The conclusion has been confirmed through both theoretical derivations and numerical simulations. Combined with different criteria, an effective signal detection in S-transformation can be realized.

A MODEL FOR WHITE NOISE ANALYSIS IN P-ADIC NUMBER FIELDS

We propose a simple model for white noise analysis in the p-adic case based on the p-adic analogue of the space L(2)(R(infinity), d mu).

Robustness of reinforced gradient-type iterative learning control for batch processes with Gaussian noise

In this paper,a reinforced gradient-type iterative learning control pro file is proposed by making use of system matrices and a proper learning step to improve the tracking performance of batch processes disturbed by external Gaussian white noise.The robustness is analyzed and the range of the step is speci fied by means of statistical technique and matrix theory.Compared with the conventional one,the proposed algorithm is more ef ficient to resist external noise.Numerical simulations of an injection molding process illustrate that the proposed scheme is feasible and effective.

Effect of Gaussian Noise Amplitude on Translation Error Estimated Using Double-Wayland Algorithm

The Wayland algorithm has been improved in order to evaluate the degree of visible determinism for dynamical systems that generate time series. The objective of this study is to show that the Double-Wayland algorithm can distinguish between time series generated by a deterministic process and those generated by a stochastic process. The authors conducted numerical analysis of the van der Pol equation and a stochastic differential equation as a deterministic process and a Ganssian stochastic process, respectively. In case of large S/N ratios, the noise term did not affect the translation error derived from time series data, but affected that from the temporal differences of time series. In case of larger noise amplitudes, the translation error from the differences was calculated to be approximately 1 using the Double-Wayland algorithm, and it did not vary in magnitude. Furthermore, the translation error derived from the differenced sequences was considered stable against noise. This novel algorithm was applied to the detection of anomalous signals in some fields of engineering, such as the analysis of railway systems and bio-signals.

Recovery of Transient Signals in Noise by OptimalThresholding in Wavelet Domain

：研究用离散子波变换复原被加性高斯白噪声污染的瞬态信号．在子波域中提出了一种最佳门限方法，该方法涉及到对于波系数的假设检验，利用似然比、奈曼，皮尔逊准则和最小均方差设计该门限，计算机仿真证明，该方法在较低信噪比下复原信号的有效性．

Stochastic response of fractional-order van der Pol oscillator

We studied the response of fractional-order van de Pol oscillator to Gaussian white noise excitation in this letter. An equivalent integral-order nonlinear stochastic system is obtained to replace the given system based on the principle of minimum mean-square error. Through stochastic averaging, an averaged Ito equation is deduced. We obtained the Fokker–Planck–Kolmogorov equation connected to the averaged Ito equation and solved it to yield the approximate stationary response of the system. The analytical solution is confirmed by using Monte Carlo simulation.

Noise-Induced Transition in a Voltage-Controlled Oscillator Neuron Model

In the presence of Gaussian white noise,we study the properties of voltage-controlled oscillator neuronmodel and discuss the effects of the additive and multiplicative noise.It is found that the additive noise can accelerate andcounterwork the firing of neuron,which depends on the value of central frequency of neuron itself,while multiplicativenoise can induce the continuous change or mutation of membrane potential.

NOISE-INDUCED CHAOTIC MOTIONS IN HAMILTONIAN SYSTEMS WITH SLOW-VARYING PARAMETERS

This paper studies chaotic motions in quasi-integrable Hamiltonian systems with slow-varying parameters under both harmonic and noise excitations. Based on the dynamic theory and some assumptions of excited noises, an extended form of the stochastic Melnikov method is presented. Using this extended method, the homoclinic bifurcations and chaotic behavior of a nonlinear Hamiltonian system with weak feed-back control under both harmonic and Gaussian white noise excitations are analyzed in detail. It is shown that the addition of stochastic excitations can make the parameter threshold value for the occurrence of chaotic motions vary in a wider region. Therefore, chaotic motions may arise easily in the system. By the Monte-Carlo method, the numerical results for the time-history and the maximum Lyapunov exponents of an example system are finally given to illustrate that the presented method is effective.

A Novel Coding Method Based on Fuzzy Vector Quantization for Noised Image

In this paper a novel coding method based on fuzzy vector quantization for noised image with Gaussian white-noise pollution is presented. By restraining the high frequency subbands of wavelet image the noise is significantly removed and coded with fuzzy vector quantization. The experimental result shows that the method can not only achieve high compression ratio but also remove noise dramatically.

THE REGULARIZED SOLUTION APPROXIMATION OF FORWARD/BACKWARD PROBLEMS FOR A FRACTIONAL PSEUDO-PARABOLIC EQUATION WITH RANDOM NOISE

This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.

MAXIMUM LIKELIHOOD SOURCE SEPARATION FOR FINITE IMPULSE RESPONSE MULTIPLE INPUT-MULTIPLE OUTPUT CHANNELS IN THE PRESENCE OF ADDITIVE NOISE

Blind identification-blind equalization for Finite Impulse Response (FIR) Multiple Input-Multiple Output (MIMO) channels can be reformulated as the problem of blind sources separation. It has been shown that blind identification via decorrelating sub-channels method could recover the input sources. The Blind Identification via Decorrelating Sub-channels(BIDS)algorithm first constructs a set of decorrelators, which decorrelate the output signals of subchannels, and then estimates the channel matrix using the transfer functions of the decorrelators and finally recovers the input signal using the estimated channel matrix. In this paper, a new approximation of the input source for FIR-MIMO channels based on the maximum likelihood source separation method is proposed. The proposed method outperforms BIDS in the presence of additive white Gaussian noise.

Slowing down critical transitions via Gaussian white noise and periodic force

Stochastic perturbations and periodic excitations are generally regarded as sources to induce critical transitions in complex systems. However, we find that they are also able to slow down an imminent critical transition. To illustrate this phenomenon, a periodically driven bistable eutrophication model with Gaussian white noise is introduced as a prototype class of real systems.The residence probability(RP) is presented to measure the possibility that the given system stays in the oligotrophic state versus Gaussian white noise and periodic force. Variations in the mean first passage time(MFPT) and the mean velocity(MV) of the first right-crossing process are also calculated respectively. We show that the frequency of the periodic force can increase the MFPT while reduce the MV under different control parameters. Nevertheless, the noise intensity or the amplitude may result in an increase of the RP only in the case of control parameters approaching the critical values. Furthermore, for an impending critical transition, an increase of the RP appears with the interaction between the amplitude and noise intensity or the combination of the noise intensity and frequency, while the interaction of the frequency and amplitude leads to an extension of the MFPT or a decrease of the MV. As a result, an increase of the RP and MFPT, and a decrease of the MVobtained from our results claim that it is possible to slow down an imminent critical transition via Gaussian white noise and periodic force.

Stochastic Stability of FitzHugh-Nagumo Systems in Infinite Lattice Perturbed by Gaussian White Noise

The current paper is devoted to the study of stochastic stability of FitzHugh-Nagumo systems in infinite lattice perturbed by Gaussian white noise. We first study the dynamics of stochastic FitzHugh-Nagumo systems, then prove the existence and uniqueness of their equilibriums, which mix exponentially. Finally, we investigate asymptotic behavior of equilibriums when the size of noise gets to zero.

Denoising of Medical Images Using Multiwavelet Transforms and Various Thresholding Techniques

The problem of estimating an image corrupted by additive white Gaussian noise has been of interest for practical reasons. Non-linear denoising methods based on wavelets, have become popular but Multiwavelets outperform wavelets in image denoising. Multiwavelets are wavelets with several scaling and wavelet functions, offer simultaneously Orthogonality, Symmetry, Short support and Vanishing moments, which is not possible with ordinary (scalar) wavelets. These properties make Multiwavelets promising for image processing applications, such as image denoising. The aim of this paper is to apply various non-linear thresholding techniques such as hard, soft, universal, modified universal, fixed and multivariate thresholding in Multiwavelet transform domain such as Discrete Multiwavelet Transform, Symmetric Asymmetric (SA4), Chui Lian (CL), and Bi-Hermite (Bih52S) for different Multiwavelets at different levels, to denoise an image and determine the best one out of it. The performance of denoising algorithms and various thresholding are measured using quantitative performance measures such as, Mean Square Error (MSE), and Root Mean Square Error (RMSE), Signal-to-Noise Ratio (SNR), Peak Signal-to-Noise Ratio (PSNR). It is found that CL Multiwavelet transform in combination with modified universal thresholding has given best results.

变截面压电悬臂梁能量采集器在高斯白噪声激励下的稳态统计特性研究

环境振动是一种非周期、随机的宽频激励,研究振动能量采集器在环境振动下的能量采集特性具有重要意义。本文采用改进随机平均法,求解了变截面压电梁在高斯白噪声激励下的等效振幅、位移、速度的稳态概率密度函数,位移与速度的联合概率密度函数以及稳态均方输出电压,随后研究了变截面压电梁的能量采集效能。结果表明:负载电阻一定时,截面系数β>0时的变截面压电梁相比β=0时的等截面压电梁有更好的稳态均方输出电压;截面系数β>0时,随着电阻电容乘积的倒数的增加,变截面压电梁的均方电压均呈现逐渐减小的趋势,当电阻电容乘积的倒数值一定时,β值越大,均方电压也越高;随着噪声强度的增加,变截面压电梁的均方电压均呈现逐渐增大的趋势,当噪声强度一定时,β值越大,均方电压也越高。本文研究结果可为变截面压电悬臂梁能量采集系统的设计及应用提供理论依据。