Correlation function of the amplitude and of the intensity fluctuation for a laser model near threshold

In extension of a preceding paper the correlation function of the amplitude and of the intensity fluctuation are calculated in the threshold region. The laser amplitude is treated as a classical random variable obeying a van der Pol equation with a noise term. In order to get correlation functions, the method of distribution functions is employed. The distribution functions are evaluated by the Fokker-Planck equation. The lowest eigensolutions of the Fokker-Planck equation are obtained approximately by a variational method.     

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.     

A statistical method for characterizing the noise in nonlinearly reconstructed images from undersampled MR data: The POCS example

The projection-onto-convex-sets (POCS) algorithm is a powerful tool for reconstructing high-resolution images from undersampled k-space data. It is a nonlinear iterative method that attempts to estimate values for missing data. The convergence of the algorithm and its other deterministic properties are well established, but relatively little is known about how noise in the source data influences noise in the final reconstructed image. In this paper, we present an experimental treatment of the statistical properties in POCS and investigate 12 stochastic models for its noise distribution beside its nonlinear point spread functions. Statistical results show that as the ratio of the missing k-space data increases, the noise distribution in POCS images is no longer Rayleigh as with conventional linear Fourier reconstruction. Instead, the probability density function for the noise is well approximated by a lognormal distribution. For small missing data ratios, however, the noise remains Rayleigh distributed. Preliminary results show that in the presence of noise, POCS images are often dominated by POCS-enhanced noise rather than POCS-induced artifacts. Implicit in this work is the presentation of a general statistical method that can be used to assess the noise properties in other nonlinear reconstruction algorithms.     

Array gain of fourth-order cumulants beamforming under typical probability density background

The fourth-order cumulant of zero mean Gaussian distribution noise always equals to zero theoretically.In practice the probability density of noise and reverberation is the key problem to performance of the fourth-order cumulant beamforming technique.In this paper,the array gain functions of the fourth-order cumulant beamforming are deducted considering the instantaneous amplitude distribution of the ambient sea noise and bottom reverberation respectively.And the relationships are determined between array gain and the factors including the number of the array elements,the fourth-order and second-order statistical properties of the noise and reverberation,and the input signal-to-noise ratio.It is also verified that there is a critical signal-to-interference ratio and the fourth-order cumulant beamforming can obtain higher gain and resolution than the conventional beamforming method when the ratio is larger than it.The results of experiment data processing demonstrate that the gain and the resolution of the fourth-order cumulant beamforming coincide with the theoretic.     

Probability distribution function for systems driven by superheavy-tailed noise

We develop a general approach for studying the cumulative probability distribution function of localized objects (particles) whose dynamics is governed by the first-order Langevin equation driven by superheavy-tailed noise. Solving the corresponding Fokker-Planck equation, we show that due to this noise the distribution function can be divided into two different parts describing the surviving and absorbing states of particles. These states and the role of superheavy-tailed noise are studied in detail using the theory of slowly varying functions.     

Relaxation problem with quadratic noise

A linear first-order equation with a quadratic colored noise is considered. An exact one-dimensional probability distribution of the process is obtained from the characteristic function. The characteristic function is calculated by means of special functionals of the noise. An auxiliary set of three ordinary differential equations (which contains a Riccati equation) is solved for all values of parameters of the problem. In peculiar cases, the characteristic function is expressed by elementary functions. Graphs of the probability density function are presented for a few cases. The article is a continuation of the author's previous paper.     

Distribution functions for the Brownian motion of particles in a periodic potential driven by an external force

The stationary distribution functions for the Brownian motion of particles driven by an external force are calculated by expanding the velocity part into Hermite functions and the space part into a Fourier series. Insertion into the Fokker-Planck equation leads to a matrix continued fraction for the lowest two coefficients of the Hermite functions. Higher order terms are found by reverse iteration. Results are shown for a cosine potential. The good convergence allows the calculation in the full range of damping constants. For small friction the distribution function is in good agreement with previous results and the maxima are given by the solutions without noise.     

Characterizing auditory neurons using the Wigner and Rihacek distributions: a comparison

Because of their dynamic properties, most sounds can best be characterized in the combined frequency-time (FT) domain. Powerful frequency-time characterizations are the Wigner distribution function (WDF) and the Rihacek energy density function (RDF). In the present paper several new concepts are introduced such as using the WDF to characterize the tuning of auditory neurons under wideband noise stimulation and a new method to quantify phase lock of auditory neurons to a wideband noise. No appreciable differences were found between the WDF and RDF in narrow-band signal representations. However, the differences between the WDF and RDF increase as the bandwidth of the signal increases. When signals are buried in uncorrelated background noise, the average FT function of these signals may be obtained through averaging the FT functions for each signal plus noise segment. The WDF takes at least a factor 2 more in time to compute than the RDF. The FT functions can be used to characterize (linear) filters by averaging FT functions of input-noise segments that precede threshold crossings of the filter's output signal. Both the WDF and the RDF were used to characterize auditory neurons from the midbrain in anurans; the WDF always had a smaller bandwidth than the RDF. By comparing the spectrum of the reverse correlation function and the average spectrum of the noise segments preceding the spikes, a quantification of the amount of phase lock of the auditory neuron to the noise is obtained.     

A passive inverse filter for Green's function retrieval

Passive methods for the recovery of Green's functions from ambient noise require strong hypotheses, including isotropic distribution of the noise sources. Very often, this distribution is nonisotropic, which introduces bias in the Green's function reconstruction. To minimize this bias, a spatiotemporal inverse filter is proposed. The method is tested on a directive noise field computed from an experimental active seismic data set. The results indicate that the passive inverse filter allows the manipulation of the spatiotemporal degrees of freedom of a complex wave field, and it can efficiently compensate for the noise wavefield directivity.     

Measurement of radial and circumferential modes in annular and circular fan ducts

The distribution of acoustic energy among the modes in a duct is important in determining the source distribution, the radiation characteristics and the effect of any acoustic linings. This distribution can be determined by processing the microphone signals obtained over planes perpendicular to the duct axis. In an annular or circular duct, the circumferential analysis is simply a Fourier transform, but the radial analysis is in terms of Bessel functions. Methods of determining the radial mode distribution are discussed and results of such analyses on idealized distributions are presented. The use of the most suitable methods of analysis is then demonstrated in measuring the modal distribution of the distortion generated noise of an isolated fan.     

基于基函数展开方法处理具有陡峭界面的Abel反演问题

在激光聚变研究中,存在大量具有陡峭不连续界面特性的靶丸等离子体诊断问题,需要借助Abel反演方法对结果进行分析。 提出了一种基于基函数展开处理不连续径向分布的Abel反演方法,采用带约束的Landweber迭代法求得优化结果。利用该算法可以对不连续阶跃分布进行比较准确的反演,获得阶跃结构特征。在理想情况下,针对不连续阶跃分布的反演方差好于10-4,即使在存在一定噪声的情况下也仍然可以获得较好的结果。该方法可用于对激光聚变研究中压缩过程中球壳的背光照相、自发光成像、光谱测量等诊断结果的数据分析。     

Quantum mechanical theory of fluctuations and relaxation in semiconductor lasers

Pumping, spontaneous emission and electron-electron scattering lead to relaxation terms in the mean equations of motion for the electron system. These terms are derived from a quantum mechanical basis by second order perturbation theory and by appropriate reservoir averaging. If the electron distribution is not too strongly degenerate, then a relaxation time approximation can be derived. The quantum mechanical Langevin method is used to include noise. The correlation functions of all fluctuation operators are calculated. From the knowledge of the equations of motion and of the correlation functions it is possible to calculate the noise properties of the laser light and of the junction current, as will be shown in other publications.     

Joint Probability Distribution of the System Driven by Internal and External Noises Simultaneously

We obtain the equation for the steady state joint probability distribution of the system driven by external and internal noises simultaneously, where external noise is the dichotomous noise and internal noise is the Gaussian white noise. As to the application of our equation, we discuss two examples for which the correlation functions and associated relaxation times are calculated. We find the coupling effect of the external and the internal noises for the relaxation time.     

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.     

A simplified method for detecting information on linear correlation latent in random noise or vibration waves

It is well-known that linear correlation information is very useful in establishing the statistical properties of random noise or vibration waves. As the amount of data increases, however, calculating the linear correlation function by the usual multiplicative operations for large amounts of data can be very troublesome, and so some simplified practical methods of detecting the correlation function are desirable. In this paper, a practical method of detection of a linear correlation function latent in random noise or vibration waves is proposed, based on use of the conditional probability distribution. First, a general expression for the bivariate joint probability distribution for discrete level sampling is introduced in the form of a series expansion in orthonormal functions. The expansion coefficients give principally the information on linear and non-linear correlations, so that a general expression for the correlation function can be derived by conditional averaging. A new simplified version of this detection method is then presented, which does not require higher order statistical information. Finally, the effectiveness of the method is confirmed experimentally by applying it to some actual street noise in Hiroshima City.     

Some factors affecting the magnitude of comodulation masking release

This paper examines some of the factors that can affect the magnitude of comodulation masking release (CMR). In experiment I, psychometric functions were measured for the detection of a 1-kHz sinusoidal signal in a "multiplied" narrow-band noise centered at 1 kHz (reference condition) and the same noise with two comodulated flanking bands added. The functions were slightly steeper for the comodulated than for the reference masker. Thus CMRs measured at a high percent correct point were slightly (0.4 dB) larger than CMRs measured at a low percent correct point. Large individual differences were found for the reference masker but not for the comodulated masker. Experiment II compared CMRs obtained with narrow-band Gaussian noise and multiplied noise, using a single flanking band. For a flanking band remote from the signal frequency, the CMRs were smaller and more variable for the multiplied noise than for the Gaussian noise. This variability arose mainly from individual differences in the reference condition. Experiment III compared growth-of-masking functions for a signal centered in Gaussian noise and multiplied noise. Thresholds were lower for the multiplied than for the Gaussian noise, and the differences were greatest at high noise levels. The results are consistent with the idea that, for multiplied noise, some subjects can detect a change in the distribution of the envelope of the stimulus, when the signal is added to the masker. Such subjects have low thresholds in the reference condition, and give small CMRs. Other subjects are relatively insensitive to this cue. They have higher thresholds in the reference condition, and give larger CMRs. For Gaussian noise, thresholds for the reference condition are relatively stable across subjects and CMRs tend to be substantial, even for flanking-band frequencies remote from the signal frequency.     

Model independent control of lightly damped noise/vibration systems

Feedforward control is a popular strategy of active noise/vibration control. In well-damped noise/vibration systems, path transfer functions from actuators to sensors can be modeled by finite impulse response (FIR) filters with negligible errors. It is possible to implement noninvasive model independent feedforward control by a recently proposed method called orthogonal adaptation. In lightly damped noise/vibration systems, however, path transfer functions have infinite impulse responses (IIRs) that cause difficulties in design and implementation of broadband feedforward controllers. A major source of difficulties is model error if IIR path transfer functions are approximated by FIR filters. In general, active control performance deteriorates as model error increases. In this study, a new method is proposed to design and implement model independent feedforward controllers for broadband in lightly damped noise/vibration systems. It is shown analytically that the proposed method is able to drive the convergence of a noninvasive model independent feedforward controller to improve broadband control in lightly damped noise/vibration systems. The controller is optimized in the minimum H2 norm sense. Experiment results are presented to verify the analytical results.     

非高斯Lévy噪声驱动下的非对称双稳系统的相转移和平均首次穿越时间

研究了非高斯Lévy噪声激励下非对称双稳系统的相转移和首次穿越问题.首先利用Grünwald-Letnikov有限差分方法数值求解系统所对应的分数阶Fokker-Plank方程,得到了系统的稳态概率密度函数.然后分析了系统的非对称参数以及噪声强度和稳定性指标对稳态概率密度函数的影响,发现了非对称参数和稳定性指标的变化都能够诱导系统发生相转移.进一步研究了系统的平均首次穿越时间,得到了非对称参数、噪声强度和稳定性指标影响系统平均首次穿越时间的不同作用机理. 关键词： 非高斯Lévy噪声 非对称双稳系统 相转移 平均首次穿越时间     

Use of error diffusion with space-variant optimized weights to obtain high-quality quantized images and holograms

Error diffusion is an important procedure for image and hologram quantization. The spatial distribution of the spectrum of the quantization noise is shaped by a filter function, which depends on the diffusion weights. The customary weights applied during the whole quantization process are optimized to yield the desired filter functions. Stability restrictions limit the optimization process. We suggest optimizing new weights locally after the quantization of each pixel. In this way the eventual occurrence of instabilities can be counteracted and the quality of the filter function improved.     

Backscattering grain noise modelling in ultrasonic non-destructive testing

Abstract

Many materials present an internal grain microstructure. When these materials are subjected to ultrasonic non-destructive testing, the grains behave like scattering centres producing unwanted backscattered noise that can make the detection of true defects difficult. This paper is devoted to the modelling of the probability density and the spacetime correlation functions of the grain noise complex envelope. Assuming statistical independence between any pair of grains, the authors derive analytical expressions for the above functions. Specifically, the envelope comes to be K-distributed, the parameters of the distribution may be related, under reasonable simplifying assumptions, to the material characteristics (grain density, grain size distribution, propagation velocity). The spacetime correlation function is a separable function. It may be expressed as the product of a spatial factor due to the spatial correlation introduced by the non-zero beamwidth, and a time factor due to the time correlation introduced by the non-zero pulse duration. The analytical expressions are verified by means of real data measured in austenitic stainless steel specimens.