Characterization of Pressure Signals in Fluidized Beds Loaded with Large Particles Using Wigner Distribution Analysis: Feasibility of Diagnosis of Agglomeration

An experimental verification is reported on the early predicting index of agglomeration in bubbling fluidized bed. Coarse quartz sand, which has the same density but larger diameter than the bed material, was used to simulate the initial agglomerated particle. Wigner distribution was used to analyze the pressure fuctuation of the tested bed, and the average amplitude of local domain frequency （LDF） and local peak weighted average frequency （LPWA） under different operating conditions were measured and compared. The results showed that the LDF is sensitive to the agglomeration phenomena and had quick response to the incipient agglomeration in fluidized beds. It can be concluded from the results that these two parameters could be taken as the characteristic indexes to the agglomeration in fuidized beds.

Wigner-Ville distribution and cross Wigner-Ville distribution of noisy signals

The Wigner-Ville distribution （WVD） and the cross Wigner-Ville distribution （XWVD） have been shown to be efficient in the estimation of instantaneous frequency （IF）. But the statistical result of the IF estimation from XWVD peak is much better than using WVD peak. The reason is given from a statistical point of view. Theoretical studies show that XWVD of the analyzed signal can be estimated from XWVD of the noise-contaminated signal. The estimation is unbiased, and the variance is equal to that of noise. In this case, WVD cannot be estimated from W-VD of the noise-contaminated signal. Therefore, higher SNR is required when WVD is used to analyze signals.

Feature Extraction Method Based on Pseudo-Wigner-Ville Distribution for Rotational Machinery in Variable Operating Conditions

In the case of fault diagnosis for roller bearings, the conventional diagnosis approaches by using the time interval of energy impacts in time-frequency distribution or the pass-frequencies are based on the assumption that machinery operates under a constant rotational speed. However, when the rotational speed varies in the broader range, the pass-frequencies vary with the change of rotational speed and bearing faults cannot be identified by the interval of impacts. Researches related to automatic diagnosis for rotational machinery in variable operating conditions were quite few. A novel automatic feature extraction method is proposed based on a pseudo-Wigner-Ville distribution （PWVD） and an extraction of symptom parameter （SP）. An extraction method for instantaneous feature spectrum is presented using the relative crossing information （RCI） and sequential inference approach, by which the feature spectrum from time-frequency distribution can be automatically, sequentially extracted. The SPs are considered in the frequency domain using the extracted feature spectrum to identify among the conditions of a machine. A method to obtain the synthetic symptom parameter is also proposed by the least squares mapping （LSM） technique for increasing the diagnosis sensitivity of SP. Practical examples of diagnosis for bearings are given in order to verify the effectiveness of the proposed method. The verification results show that the features of bearing faults, such as the outer-race, inner-race and roller element defects have been effectively extracted, and the proposed method can be used for condition diagnosis of a machine under the variable rotational speed.

Wigner Function of Density Operator for Negative Binomial Distribution

By using the technique of integration within an ordered product （IWOP） of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator.

Statistical Performance of the Wigner-Ville Distribution and the Cross Wigner-Ville Distribution

This paper analyzes statistical performances of the Wigner-Ville distribution (WVD) and the cross Wigner-Ville distribution (XWVD). Theoretical studies show that XWVD of the analyzed signal can be estimated from XWVD of the noise-contaminated signal . The estimation is unbiased, and the variance is equal to that of noise. In this case, WVD cannot be estimated from WVD of the noise-contaminated signal . Therefore higher SNR is required when using WVD.

Improvement on polynomial Wigner-Ville distribution for detecting higher-order polynomial phase signal

To detect higher order polynomial phase signals （HOPPSs）, the smoothed-pseudo polynomial Wigner-Ville distribution （SP-PVCVD）, an improved version of the polynomial Wigner-Ville distribution （PVCVD）, is presented using a separable kernel. By adjusting the lengths of the functions in the kernel, the balance between resolution retaining and interference suppressing can be adjusted conveniently. The proposed method with merits of interference terms reduction and noise suppression can provide time frequency representation of better readability and more accurate instantaneous frequency （IF） estimation with higher order SP-PVfVD. The performance of the SP-PWVD is verified by computer simulations.

SORTING RADAR SIGNAL BASED ON WAVELET CHARACTERISTICS OF WIGNER-VILLE DISTRIBUTION

Common sorting method have low sorting rates and is sensitive to the Signal-to-Noise Ratio(SNR),wavelet characteristics of Wigner-Ville distribution are applied to sort unknown complicated radar signal,high sorting accuracy can be got.The Wigner-Ville distribution of received signal is calculated,then it is predigested to two-dimensional characteristics.Using wavelet transformation to extract characteristics from two-dimensional of Wigner-Ville distribution,the best characteristics are selected to be used as sorting parameters.Experiment results demonstrated that the characteristics of eight typical radar emitter signals extracted by this method showed good performance of noise-resistance and clustering at large-scale SNR.

Relations between chirp transform and Fresnel diffraction,Wigner distribution function and a fast algorithm for chirp transform

Two physical interpretations of chirp transform related to Fresnel diffraction and Wigner distribution function are given. The chirp transform can be regarded as a Fresnel diffraction observed on a spherical tangent to the diffraction plane, or a rotation and stretching transformation of the Wigner distribution function space. A general fast algorithm for the numerical calculation of chirp transform is developed by employing two fast Fourier transform algorithms. The algorithm, by which a good evaluation can be achieved, unifies the calculations of Fresnel diffraction, arbitrary fractional- order Fourier transforms and other scalar diffraction systems. The algorithm is used to calculate the Fourier transform of a Gaussian function and the Fourier transform, the Fresnel transform, the Fractional-order Fourier transforms of a rectangle function to evaluate the performance of this algorithm. The calculated results are in good agreement with the analytical results, both in the amplitude and phase.

The Wigner distribution function of a super Lorentz–Gauss SLG_(11) beam through a paraxial ABCD optical system

An orthonormal beam family of super Lorentz-Gauss （SLG） beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simplest case of the SLG beams, where there are four mutually orthogonal SLG beams, namely SLG00, SLG01, SLG10, and SLGll beams. The SLG00 beam is just the Lorentz-Gauss beam. Based on the Collins integral formula and the Hermite-Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function （WDF） of an SLG11 beam through a paraxial ABCD optical system is derived. The properties of the WDF of an SLG11 beam propagating in free space are demonstrated. The normalized WDFs of an SLG11 beam at the different spatial points are depicted in several observation planes. The influence of the beam parameter on the WDF of an SLGI 1 beam in free space is analyzed at different propagation distances. The second-order moments of the WDF of an SLG11 beam in free space are also examined. This research reveals the propagation properties of an SLGll beam from another perspective. The WDFs of SLG01 and SLG10 beams can be easily obtained by using the WDFs of Lorentz-Gauss beam and the SLG11 beam.

A new finite-dimensional thermal coherent state and its Wigner distribution function

This paper constructs a new type of finite-dimensional thermal coherent states （FDTCS）, which differs from the proceeding thermal coherent state in construction, as realisations of SU（2） Lie algebra. Using the technique of integration within an ordered product of operator, it investigates the orthonormality and completeness relation of the FDTCS. Based on the thermal Wigner operator in the thermal entangled state representation, the Wigner function of the FDTCS is obtained. The nonclassical properties of the FDTCS are discussed in terms of the negativity of its Wigner function.

Continuous Multipartite Entangled Representation and Its Wigner Operator and Marginal Distribution

By extending the EPR bipartite entanglement to multipartite case, we briefly introduce a continuous multipartite entangled representation and its canonical conjugate state in the multi-mode Fock space, analyze their Schmidt decompositions and give their entangling operators. Furthermore, based on the above analysis we also find the n-mode Wigner operator. In doing so we may identify the physical meaning of the marginal distribution of the Wigner function.

Generalized Wigner Operator and Bivariate Normal Distribution in p-q Phase Space

We introduce a kind of generalized Wigner operator,whose normally ordered form can lead to the bivariatenormal distribution in p-q phase space.While this bivariate normal distribution corresponds to the pure vacuum state inthe generalized Wigner function phase space,it corresponds to a mixed state in the usual Wigner function phase space.

Wigner Function and Phase Probability Distribution of q-Analogue of Squeezed One-Photon State

In this paper, in terms of the technique of integration within an ordered product （IWOP） of operators and the properties of the inverses of q-deformed annihilation and creation operators, normalizable q-analogue of the squeezed one-photon state, which is quite different from one introduced by Song and Fan [Int. 3. Theor. Phys. 41 （2002） 695], is constructed. Moreover, the Wigner function and phase probability distribution of q-analogue of the squeezed one-photon state are examined.

LOCALIZED RADON-WIGNER TRANSFORM AND GENERALIZED-MARGINAL TIME-FREQUENCY DISTRIBUTIONS

This paper introduces the localized Radon transform (LRT) into time-frequency distributions and presents the localized Radon-Wigner transform (LRWT). The definition of LRWT and a fast algorithm is derived, the properties of LRWT and its relationship with Radon-Wigner transform, Wigner distribution (WD), ambiguity function (AF), and generalized-marginal time-frequency distributions are analyzed.

Momentum Distribution Functions in Quark-Gluon Plasma

Based on the constituent quasiparticle model of the quark-gluon plasma (QGP), the Wigner function is presented in the form of a color path integral. The Monte Carlo calculations of the quark and gluon densities, pair correlation functions and the momentum distribution functions for strongly coupled QGP plasma in thermal equilibrium at barion chemical potential equal to zero have been carried out. Analysis of the pair correlation functions points out on arising glueballs and related gluon bound states. Comparison results between the momentum distribution functions and Maxwell-Boltzmann distributions show the significant influence of the interparticle interaction on the high energy asymptotics of the momentum distribution functions resulting in the appearance of quantum “tails”.

采用STFT-Wigner变换抑制Wigner-Ville分布交叉项

对于多分量非平稳信号分析,维格纳时频分布Wigner-Ville(WVD)存在严重的交叉项干扰。而GWT避免了Wigner-Ville分布的交叉项干扰而且具有良好的时频聚集性。但由于Gabor变换的时频聚集性不佳,当多分量信号进行Gabor变换时如果信号中各分量频率混叠,Gabor Wigner transform(GWT)就不能得到理想的结果。提出一种改进的STFT-Wigner算法,可以有效的抑制交叉项,并保持较高的时频聚集性。通过分析仿真信号和实测振动信号表明该方法能够取得良好的效果。

基于Wigner-Ville分布与小波尺度谱融合的时频特征提取方法

时频分布提供了信号特征在时间域和频率域的联合分部信息。作为两种典型的时频分布表示方法,Wigner-Ville分布(WVD)和尺度谱都存在的缺陷,体现在WVD存在严重的交叉项,尺度谱时频聚集性差。在WVD和尺度谱的基础上提出一种以消除交叉项和保持高分辨率为目的的时频特征融合算法。仿真分析验证了该算法能够有效抑制交叉项,可以很好地保持时频分辨率,且抑制了弱噪声对于时频特征的干扰。通过仿真信号的分析将该算法与Cohen类时频分析方法进行比较,验证了其在时频特征表示方面的优越性。将时频融合算法应用于轴承振动信号的时频表示,结果表明该方法能基本消除时频特征表示中的交叉项且保持了较高的时频分辨率,验证了算法在信号特征表示方面的有效性。

基于EMD-Wigner-Ville的内燃机振动时频分析

在分析多分量信号时,WVD交叉项的出现极大干扰了对信号的时频分析,针对现有WVD交叉项抑制方法存在聚集性与交叉项成分抑制相互矛盾的问题,提出了一种基于经验模态分解(EMD)的WVD交叉项抑制方法。该方法首先利用EMD分解方法,将信号分解成相互独立的一系列具有不同特征时间尺度的固有模态函数(IMF),然后运用相关系数法对经验模式分解伪分量进行剔除,再对每个IMF进行Wigner-Ville分析,最后把各个IMF的Wigner-Ville分析结果线性叠加重构原始信号的时频分布。仿真实验结果表明,该方法既能有效抑制时频分布的交叉项,又保证了Wigner-Ville分布的时频聚集性。将EMD-Wigner-Ville应用在内燃机振动时频分析中,两个实例有效地揭示出了内燃机振动信号的特征信息,克服了HHT时频分布、Wigner-Ville时频分布在分析内燃机振动信号时的缺陷,是一种有效的时频分析方法。

局部放电脉冲的Wigner时频分布特性研究

为了提高时频分布的分析精度和有效性,笔者根据局部放电脉冲信号的非平稳特性,提出使用联合时频分布对其进行处理,从而分析脉冲信号的时频特性。针对目前在非平稳信号处理中广泛使用、属于Cohen类的Wigner-Ville分布(WVD),笔者以仿真脉冲为对象,分别研究了其原始WVD、平滑伪Wigner分布(SPWVD)以及重排平滑伪Wigner分布(RSPWVD)。分析结果表明:WVD能够对局部放电脉冲信号引发的短时变化具有高度的敏感性,更适合表征非平稳信号的时变信息;SPWVD能消除双线性函数引起的交叉干扰项,但是以牺牲分布的时频分辨率为代价的;RSPWVD具有很好的时频聚集性,易于提取单个脉冲波形的时频特征参数,从而用于放电类型的模式识别以及深入研究绝缘系统中的局部放电机理。