Effects of strong noise on attractors of dynamical systems

Stationary solutions of the Fokker-Planck equation are found by expansions of the probability distribution with respect to the reciprocal noise strength. It is shown that this expansion is convergent. Explicit representations for the probability distribution are obtained by numerical simulations for the Lorenz model and for a model of generators with inertial nonlinearity (GIN). The obtained distributions show an increasing amount of fine structure with decreasing noise which more and more reflects the fractal attractor structure. Results of measurements of the power spectrum of the GIN and of the distribution in the phase space are presented in dependence on the noise strengths.     

Audience noise in concert halls during musical performances

Noise generated by the audience during musical performances is audible and sometimes disturbing. In this study, an attempt to estimate such audience noise was carried out. From the recordings of performances in five performance spaces (four concert halls and one opera house), probability density functions of the sound pressure levels were obtained in octave bands, which were fitted with three Gaussian distribution curves. The Gaussian distribution curve with the lowest mean value corresponds to a mixture of the technical background noise and audience generated noise, which is named the mixed background noise. Finally, the audience noise distribution is extracted by energy subtraction of the technical background noise levels measured in an empty condition from the mixed background noise levels. As a single index, L(90) of the audience noise distribution is named the audience noise level. Empirical prediction models were made using the four orchestra concert halls, revealing that the audience noise level is significantly correlated with the technical background noise level. It is therefore concluded that a relaxation of the current background noise recommendations for concert halls is not recommended.     

On the prediction of impact noise,part VI: Distribution of acceleration noise with frequency with application to bottle impacts

The spectral distribution of the acceleration noise, as defined in Part I of this series, is obtained using both the pressure waveform expressions and the spatial averaged velocity on the surface of the body, together with a radiation efficiency associated with the rigid body movement of the object. This distribution with frequency is shown to be mainly dependent on the size of the body and the duration of the transient and is independent of the body shape detail and the exact shape of the transient. The spectral distribution of acceleration noise is important in the case of impact of structures whose first ringing natural frequency is within the frequency range under investigation. Under such circumstances, it is important to estimate the response of the structure below this resonant frequency. In this paper this is investigated to show that the response, and hence the noise radiated from a structure below the first ringing frequency, is low and the noise in this frequency range is mostly due to acceleration noise. These results are verified in the case of bottle clashes.     

Distributions of singular values for some random matrices

The singular value decomposition is a matrix decomposition technique widely used in the analysis of multivariate data, such as complex space-time images obtained in both physical and biological systems. In this paper, we examine the distribution of singular values of low-rank matrices corrupted by additive noise. Past studies have been limited to uniform uncorrelated noise. Using diagrammatic and saddle point integration techniques, we extend these results to heterogeneous and correlated noise sources. We also provide perturbative estimates of error bars on the reconstructed low-rank matrix obtained by truncating a singular value decomposition.     

The accuracy of source distributions measured by using polar correlation

The evaluation of jet noise source distributions as obtained by using the polar correlation technique is discussed. The accuracy with which this, or any other, technique can measure a jet noise source distribution is limited by the analytical model used to describe the source distribution and the statistical estimate which can be made of the randomly fluctuating source strengths. Both these problems are considered and criteria are developed for the accuracy of source location data in terms of the measurement parameters.     

含噪动态光散射测量数据反演中正则化算法与Chahine算法的比较

采用两种常用的粒度反演方法——正则化和Chahine算法,对90nm与250nm单峰分布、50nm与200nm双峰分布、100nm与300nm双峰分布的模拟动态光散射数据,以及105nm、300nm标准颗粒的实测动态光散射数据进行了反演分析.结果表明:噪声水平的高低是影响粒度分布反演准确性的关键因素之一,反演结果的准确性随噪声水平的增加而降低,噪声水平超过某一阈值后,将无法得到有意义的反演结果;不同反演方法具有不同的抗噪能力,在低噪声水平下反演结果无显著差别,随着噪声水平的增加,反演结果表现出很大差异;正则化方法通过正则参数的选择可以有效抑制噪声影响,表现出强于Chahine算法的抗噪能力;与Chahine算法相比,正则化方法不需要假定初始分布,因此,在噪声较大的实验或生产过程中进行颗粒分布测量时,宜采用正则化方法.     

用于电介质中空间电荷分布测量的Tikhonov反卷积算法

研究了使用压力波法测量平板电介质试样的空间电荷分布的数值解法,使用基于Tikhonov正则化方法的反卷积算法得到了真实的空间电荷分布.在反卷积算法中使用了相关的技术处理,如小波包过滤高频噪音,Tikhonov正则化方法处理积分方程等.利用数值实验研究了噪声对反卷积算法的影响,结果表明,在无噪或者低噪环境下,反卷积算法能够非常好地计算出电介质中的空间电荷分布;在处理有噪数据时,反卷积的结果受到明显的影响,但仍然有较高的计算精度.正则化参数α对空间电荷分布的数值解起着明显的光滑作用,但是对于解的积分值却影响不大.对实际测量数据进行处理的结果表明,反卷积算法成功地计算出了固体电介质中的空间电荷分布和电场分布.     

Mikrowellendiagnostik der Rauschtemperatur im Stickstoffplasma der Schwachstromsäule

This paper covers the calculation and measurement of the noise temperature for a stationary and axial homogeneous column plasma of a nitrogen discharge. The calculations are based on an electron energy distribution function which was obtained by the solution of the Boltzmann equation for a nitrogen plasma. In the low current column of this plasma the noise temperature was measured, using a Dicke-radiometer. The comparison between the calculated and measured values of the noise temperature shows a good agreement in the considered parameter region. Using a Maxwellian distribution, which was fitted to the real nitrogen plasma by the aid of the formulation of an energy balance for the electrons, the noise temperature was additionally determined in a approximate way and compared to the first calculations.     

双模环型激光增益噪声模型的非线性效应

讨论了一个双模环型激光增益噪声模型，其中考虑了完全饱和效应且乘法噪声由增益系数涨落引起。在共振及两模具有相同泵参数时，获得了光强联合定态分布的精确解析表达式。通过与现有的双模激光摸型（其中乘法噪声由损失系数涨落引起）的比较，发现乘法噪声系数的非线性效应减弱了乘法噪声给激光光强统计性质带来的反常特性，并且这种减弱随着乘法噪声增强或损失系数减小而愈加明显。     

射线理论下的浅海环境噪声场空间相干性分析及海底声学参数反演

基于射线理论,以简化海底模型为基础,获得了浅海噪声场空间相干性在频域上的表示方法,并用于海底声学参数反演。将风关海洋噪声看作分布在无限大平面上的点源,通过计算噪声场垂直方向上的能量分布,进一步获得空间两点噪声场频域相干性表达式。利用数值仿真验证了模型对于不同海底类型的敏感性。并结合噪声场空间两点的频域相干性海上实验数据,反演得到该处海域的底质类型,进一步获得海底声速、密度和声衰减系数。结果表明,反演得到的海底参数与实际情况符合较好,文中提出采用的这种计算方法能够有效的反映海底反射对于噪声场空间相干性的影响,并且可在一定程度上提高反演海底声学参数效率。      

Simulation and evaluation of phase noise for optical amplification using semiconductor optical amplifiers in DPSK applications

A thorough simulation and evaluation of phase noise for optical amplification using semiconductor optical amplifier (SOA) is very important for predicting its performance in differential phase-shift keyed (DPSK) applications. In this paper, standard deviation and probability distribution of differential phase noise at the SOA output are obtained from the statistics of simulated differential phase noise. By using a full-wave model of SOA, the noise performance in the entire operation range can be investigated. It is shown that nonlinear phase noise substantially contributes to the total phase noise in case of a noisy signal amplified by a saturated SOA and the nonlinear contribution is larger with shorter SOA carrier lifetime. It is also shown that Gaussian distribution can be useful as a good approximation of the total differential phase noise statistics in the whole operation range. Power penalty due to differential phase noise is evaluated using a semi-analytical probability density function (PDF) of receiver noise. Obvious increase of power penalty at high signal input powers can be found for low input OSNR, which is due to both the large nonlinear differential phase noise and the dependence of BER vs. receiving power curvature on differential phase noise standard deviation.     

Observations and modeling of deterministic properties of human heart rate variability

Simple models show that in Type-I intermittency a characteristic U-shaped probability distribution is obtained for the laminar phase length. The laminar phase length distribution characteristic for Type-I intermittency may be obtained in human heart rate variability data for some cases of pathology. The heart and its regulatory systems are presumed to be both noisy and non-stationary. Although the effect of additive noise on the laminar phase distribution in Type-I intermittency is well-known, the effect of neither multiplicative noise nor non-stationarity have been studied. We first discuss the properties of two classes of models of Type-I intermittency: (a) the control parameter of the logistic map is changed dichotomously from a value within the intermittency range to just below the bifurcation point and back; (b) the control parameter is changed randomly within the same parameter range as in the model class (a). We show that the properties of both models are different from those obtained for Type-I intermittency in the presence of additive noise. The two models help to explain some of the features seen in the intermittency in human heart rate variability.     

Moment equations for a spatially extended system of two competing species

The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamics of the two species. To describe the spatial distribution of the species we use a model based on Lotka-Volterra (LV) equations. By writing them in a mean field form, the corresponding moment equations for the species concentrations are obtained in Gaussian approximation. In this formalism the system dynamics is analyzed for different values of the multiplicative noise intensity. Finally by comparing these results with those obtained by direct simulations of the time discrete version of LV equations, that is coupled map lattice (CML) model, we conclude that the anticorrelated oscillations of the species densities are strictly related to non-overlapping spatial patterns.     

Dynamics of Gompertzian tumour growth under environmental fluctuations

We investigate the effect of correlated additive and multiplicative Gaussian white noise on the Gompertzian growth of tumours. Our results are obtained by solving numerically the time-dependent Fokker-Planck equation (FPE) associated with the stochastic dynamics. In our numerical approach we have adopted B-spline functions as a truncated basis to expand the approximated eigenfunctions. The eigenfunctions and eigenvalues obtained using this method are used to derive approximate solutions of the dynamics under study. We perform simulations to analyze various aspects, of the probability distribution, of the tumour cell populations in the transient- and steady-state regimes. More precisely, we are concerned mainly with the behaviour of the relaxation time (τ) to the steady-state distribution as a function of (i) of the correlation strength (λ) between the additive noise and the multiplicative noise and (ii) as a function of the multiplicative noise intensity (D) and additive noise intensity (α). It is observed that both the correlation strength and the intensities of additive and multiplicative noise, affect the relaxation time.     

Stochastic Resonance in a Simple Threshold Sensor System with Alpha Stable Noise

We investigate the effect of alpha stable noise on stochastic resonance in a single-threshold sensor system by analytic deduction and stochastic simulation. It is shown that stochastic resonance occurs in the threshold system in alpha stable noise environment, but the resonant effect becomes weakened as the alpha stable index decreases or the skewness parameter of alpha stable distribution increases. In particular, for Cauchy noise a nonlinear relation among the optimal noise deviation parameter, the signal amplitude and the threshold is analytically obtained and illustrated by using the extreme value condition for the output signal-to-noise ratio. The results presented in this communication should have application in signal detection and image restoration in the non-Gaussian noisy environment.     

Analysis of Statistical Properties of the Maximum Noise Eigenvalue of the Sample Correlation Matrix of an Antenna Array in the Presence of Signals

The characteristics of estimates of the angle and number coordinates of external sources of signals received by an antenna array depend on the statistical properties of internal noise. In the case of a limited sample, the estimate of the correlation matrix of the antenna-array signals has a random eigenvalue spectrum. In practice, when solving some important problems of detecting and estimating the number of signals, we should know the statistical properties of the maximum noise eigenvalue in order to choose correctly the threshold value for decision making. In this paper, we obtain an asymptotic formula for the integral distribution of the maximum noise eigenvalue of the sample correlation matrix in the presence of a high-power signal source. Using numerical simulation, we show that the obtained asymptotic distribution practically coincides with the exact distribution when the signal power exceeds the power of antenna-array internal noise by 6 to 10 dB.     

基于物体像的干涉条纹图像中散斑噪声的识别方法

散斑噪声是激光干涉时的普遍现象,其覆盖被测表面对应区域的形状信息,造成测量误差。针对斜入式激光干涉测量中散斑噪声的特点,提出一种基于物体像的散斑噪声的识别方法。该方法通过统计物体像中有效测量区域和背景区域内灰度分布的特点,自动计算出判定散斑噪声的上下阈值。基于物体像与干涉条纹图像间微米级的映射关系,得到干涉条纹图像中散斑噪声的位置。设计了相关实验,对干涉条纹图像中识别出的散斑噪声区域进行修补,消除了包裹相位图中一个条纹周期内相邻像素点间大于π的相位突变。     

机体表面湍流边界层噪声特性及预测方法研究

湍流边界层噪声是飞机巡航过程中的主要外部噪声源,对舱内噪声水平的影响尤为重要。因此,对飞机机体表面湍流边界层噪声的研究具有重要意义。本文通过试验获得了某型民机巡航过程中的湍流边界层噪声,试飞工况为3500ft/0.78、3500ft/0.7、2500ft/0.67、1500ft/0.66。对实测数据进行分析,发现湍流边界层噪声与动压、边界层厚度等参数有关。同时,利用计算流体力学的方法得到了飞机机体表面的压力分布,并分析了压力梯度对湍流边界层噪声的影响。最后,基于工程预测方法对湍流边界层噪声进行了预测,对于不存在逆压梯度的区域,预测结果与试验结果吻合较好,仅部分频段存在一定偏差。通过对模型的参数进行优化,改善了预测结果。     

非局部变分修复法去除高密度椒盐噪声

分析了中值滤波及其改进型算法在处理高密度椒盐噪声时效果不理想的原因,采用变分修复方法来去除高密度椒盐噪声,基于现有的全变差修复模型提出了非局部全变差修复模型。该模型利用椒盐噪声特点(均匀分布、灰度值为0或255),将噪声点看成是图像中遗失或是破损的点,首先在图像中寻找与噪声点邻域相似的区域,将相似区域的中心像素作为噪声点新的邻域然后对其插值,把图像降噪问题转化为图像修复问题,从而达到去除高密度噪声的目的。实验结果表明:该模型对噪声密度为90%的彩色和灰度图像去噪后,其峰值信噪比为22.85和28.77,在客观评价标准方面优于中值滤波及其改进型算法。该模型能有效去除高密度下的椒盐噪声并较好地恢复图像细节,为图像去除高密度噪声提供了一种新的途径。     

Features of temporal noise spatial localization while indexing in accordance with the 2D hadamard transform

It is shown that the 2D indexation of a communication channel 1D noise with the help of the 2D Hadamard transform makes it possible to represent the distribution of this noise in the restored image space in the form of a 2D distribution of its variance. The width of noise variance distribution depends on the extent of preservation of correlation between elements of communication channel 1D noise. It is shown that the degree of 2D spatial localization of noise in this case exceeds the degree of noise localization in the case when 1D Hadamard transform is used.