A NEW QUADRATIC TIME-FREQUENCY DISTRIBUTIONAND A COMPARATIVE STUDY OF SEVERAL POPULARQUADRATIC TIME-FREQUENCY DISTRIBUTIONS

A new quadratic time-frequency distribution (TFD) with a compound kernel is proposed and a comparative study of several popular quadratic TFD is carried out. It is shown that the new TFD with compound kernel has stronger ability than the exponential distribution (ED) and the cone-shaped kernel distribution (CKD) in reducing cross terms, meanwhile almost not decreasing the time-frequency resolution of ED or CKD.

The W transform and its improved methods for time-frequency analysis of seismic data

The conventional linear time-frequency analysis method cannot achieve high resolution and energy focusing in the time and frequency dimensions at the same time,especially in the low frequency region.In order to improve the resolution of the linear time-frequency analysis method in the low-frequency region,we have proposed a W transform method,in which the instantaneous frequency is introduced as a parameter into the linear transformation,and the analysis time window is constructed which matches the instantaneous frequency of the seismic data.In this paper,the W transform method is compared with the Wigner-Ville distribution(WVD),a typical nonlinear time-frequency analysis method.The WVD method that shows the energy distribution in the time-frequency domain clearly indicates the gravitational center of time and the gravitational center of frequency of a wavelet,while the time-frequency spectrum of the W transform also has a clear gravitational center of energy focusing,because the instantaneous frequency corresponding to any time position is introduced as the transformation parameter.Therefore,the W transform can be benchmarked directly by the WVD method.We summarize the development of the W transform and three improved methods in recent years,and elaborate on the evolution of the standard W transform,the chirp-modulated W transform,the fractional-order W transform,and the linear canonical W transform.Through three application examples of W transform in fluvial sand body identification and reservoir prediction,it is verified that W transform can improve the resolution and energy focusing of time-frequency spectra.

Sequential quadratic programming-based non-cooperative target distributed hybrid processing optimization method

The distributed hybrid processing optimization problem of non-cooperative targets is an important research direction for future networked air-defense and anti-missile firepower systems. In this paper, the air-defense anti-missile targets defense problem is abstracted as a nonconvex constrained combinatorial optimization problem with the optimization objective of maximizing the degree of contribution of the processing scheme to non-cooperative targets, and the constraints mainly consider geographical conditions and anti-missile equipment resources. The grid discretization concept is used to partition the defense area into network nodes, and the overall defense strategy scheme is described as a nonlinear programming problem to solve the minimum defense cost within the maximum defense capability of the defense system network. In the solution of the minimum defense cost problem, the processing scheme, equipment coverage capability, constraints and node cost requirements are characterized, then a nonlinear mathematical model of the non-cooperative target distributed hybrid processing optimization problem is established, and a local optimal solution based on the sequential quadratic programming algorithm is constructed, and the optimal firepower processing scheme is given by using the sequential quadratic programming method containing non-convex quadratic equations and inequality constraints. Finally, the effectiveness of the proposed method is verified by simulation examples.

Independence of the Residual Quadratic Sums in the Dispersion Equation with Noncentral χ²-Distribution

A model adequacy test should be carried out on the basis of accurate aprioristic ideas about a class of adequate models, as in solving of practical problems this class is final. In article, the quadratic sums entering into the equation of the dispersive analysis are considered and their independence is proved. Necessary and sufficient conditions of existence of adequate models are resulted. It is shown that the class of adequate models is infinite.

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.

Adaptive Time-Frequency Distribution Based on Time-Varying Autoregressive and Its Application to Machine Fault Diagnosis

The time-varying autoregressive （TVAR） modeling of a non-stationary signal is studied. In the proposed method, time-varying parametric identification of a non-stationary signal can be translated into a linear time-invariant problem by introducing a set of basic functions. Then, the parameters are estimated by using a recursive least square algorithm with a forgetting factor and an adaptive time-frequency distribution is achieved. The simulation results show that the proposed approach is superior to the short-time Fourier transform and Wigner distribution. And finally, the proposed method is applied to the fault diagnosis of a bearing , and the experiment result shows that the proposed method is effective in feature extraction.

Research on Low Voltage Series Arc Fault Prediction Method Based on Multidimensional Time-Frequency Domain Characteristics

The load types in low-voltage distribution systems are diverse.Some loads have current signals that are similar to series fault arcs,making it difficult to effectively detect fault arcs during their occurrence and sustained combustion,which can easily lead to serious electrical fire accidents.To address this issue,this paper establishes a fault arc prototype experimental platform,selects multiple commonly used loads for fault arc experiments,and collects data in both normal and fault states.By analyzing waveform characteristics and selecting fault discrimination feature indicators,corresponding feature values are extracted for qualitative analysis to explore changes in timefrequency characteristics of current before and after faults.Multiple features are then selected to form a multidimensional feature vector space to effectively reduce arc misjudgments and construct a fault discrimination feature database.Based on this,a fault arc hazard prediction model is built using random forests.The model’s multiple hyperparameters are simultaneously optimized through grid search,aiming tominimize node information entropy and complete model training,thereby enhancing model robustness and generalization ability.Through experimental verification,the proposed method accurately predicts and classifies fault arcs of different load types,with an average accuracy at least 1%higher than that of the commonly used fault predictionmethods compared in the paper.

TVAR Time-frequency Analysis for Non-stationary Vibration Signals of Spacecraft

Predicting the time-varying auto-spectral density of a spacecraft in high-altitude orbits requires an accurate model for the non-stationary random vibration signals with densely spaced modal frequency. The traditional time-varying algorithm limits prediction accuracy, thus affecting a number of operational decisions. To solve this problem, a time-varying auto regressive （TVAR） model based on the process neural network （PNN） and the empirical mode decomposition （EMD） is proposed. The time-varying system is tracked on-line by establishing a time-varying parameter model, and then the relevant parameter spectrum is obtained. Firstly, the EMD method is utilized to decompose the signal into several intrinsic mode functions （IMFs）. Then for each IMF, the PNN is established and the time-varying auto-spectral density is obtained. Finally, the time-frequency distribution of the signals can be reconstructed by linear superposition. The simulation and the analytical results from an example demonstrate that this approach possesses simplicity, effectiveness, and feasibility, as well as higher frequency resolution.

Wigner-Ville distribution and its application in seismic attenuation estimation

The attenuation of seismic signals is often characterized in the frequency domain using statistical measures of the power spectrum. However, the conventional Fourier transform-based power spectrum estimation methods suffer from time-frequency resolution problems. Wigner-Ville distribution, which is a member of Cohen class time-frequency distributions, possesses many appealing properties, such as time-frequency marginal distribution, time-frequency localization, etc. Therefore, Wigner-Ville distribution offers a new way for estimating the attenuation of seismic signals. This paper initially gives a brief introduction to Wigner-Ville distribution and the smoothed Wigner-Ville distribution that is effective in reducing the cross-term effect, and then presents a method for seismic attenuation estimation based on the instantaneous energy spectrum of the Wigner-Ville distribution. A real data example from central Tarim Basin in western China is presented to illustrate the effectiveness of the proposed method. The results show that the Wigner-Ville distribution-based seismic attenuation estimation method can effectively detect the difference between reef, shoal and lagoon facies by their attenuation properties, indicating that the estimated seismic attenuation can be used for reef and shoal carbonate reservoir characterization.

广义函数空间上Quadratic函数方程的Hyers-Ulam-Rassias型稳定性

利用热方程的核,通过对广义函数正则化的方法,给出了在广义函数空间上二次函数方程的改进的Hyers-Ulam-Rassias型稳定性定理,从而推广了文献[8]的结果.

Parametric adaptive time-frequency representation based on time-sheared Gabor atoms

A localized parametric time-sheared Gabor atom is derived by convolving a linear frequency modulated factor, modulating in frequency and translating in time to a dilated Gaussian function, which is the generalization of Gabor atom and is more delicate for matching most of the signals encountered in practice, especially for those having frequency dispersion characteristics. The time-frequency distribution of this atom concentrates in its time center and frequency center along energy curve, with the curve being oblique to a certain extent along the time axis. A novel parametric adaptive time-frequency distribution based on a set of the derived atoms is then proposed using a adaptive signal subspace decomposition method in frequency domain, which is non-negative time-frequency energy distribution and free of cross-term interference for multicomponent signals. The results of numerical simulation manifest the effectiveness of the approach in time-frequency representation and signal de-noising processing.

Quasi-LFM radar waveform recognition based on fractional Fourier transform and time-frequency analysis

Recent advances in electronics have increased the complexity of radar signal modulation.The quasi-linear frequency modulation(quasi-LFM)radar waveforms(LFM,Frank code,P1−P4 code)have similar time-frequency distributions,and it is difficult to identify such signals using traditional time-frequency analysis methods.To solve this problem,this paper proposes an algorithm for automatic recognition of quasi-LFM radar waveforms based on fractional Fourier transform and time-frequency analysis.First of all,fractional Fourier transform and the Wigner-Ville distribution(WVD)are used to determine the number of main ridgelines and the tilt angle of the target component in WVD.Next,the standard deviation of the target component's width in the signal's WVD is calculated.Finally,an assembled classifier using neural network is built to recognize different waveforms by automatically combining the three features.Simulation results show that the overall recognition rate of the proposed algorithm reaches 94.17%under 0 dB.When the training data set and the test data set are mixed with noise,the recognition rate reaches 89.93%.The best recognition accuracy is achieved when the size of the training set is taken as 400.The algorithm complexity can meet the requirements of real-time recognition.

Transmuted Exponentiated Moment Pareto Distribution

In this work, the authors proposed a four parameter potentiated lifetime model named as Transmuted Exponentiated Moment Pareto (TEMP) distribution and discussed numerous characteristic measures of proposed model. Parameters are estimated by the method of maximum likelihood and performance of these estimates is also assessed by simulations study. Four suitable lifetime datasets are modeled by the TEMP distribution and the results support that the proposed model provides much better results as compared to its sub-models.

Spatial Distribution Pattern of the Steppe Toad-headed Lizard(Phrynocephalus frontalis) and Its Influencing Factors

Spatial distribution patterns are associated with life history and behavioral adaptations of animals. For studying the spatial distribution pattern of the steppe toad-headed lizard(Phrynocephalus frontalis) and its influencing factors,we conducted experiments in Hunshandake Sandy Land in Inner Mongolia,China in July 2009. By calculating the clustered indices,we found that the lizard was aggregately distributed when the sampling quadrat was smaller than 10 m × 10 m,and uniformly distributed when it was greater than 10 m × 10 m. The Nearest Neighbor Rule showed a clustering distribution pattern for P. frontalis and the distribution pattern was quadrat-sampling dependent. Furthermore,the cluster was determined by environmental factors when the sampling quadrat was smaller than 20 m × 20 m,but it was determined by both environmental factors and characteristics of the lizard when it was larger than 20 m × 20 m. Our results suggested that the steppe toad-headed lizards tended to aggregate into suitable habitat patches in desert areas. Additionally,we discussed that the lizard aggregation could be potentially used as an indictor of movement of sand dunes.

Digital modulation classification using multi-layer perceptron and time-frequency features

Considering that real communication signals corrupted by noise are generally nonstationary, and timefrequency distributions are especially suitable for the analysis of nonstationary signals, time-frequency distributions are introduced for the modulation classification of communication signals： The extracted time-frequency features have good classification information, and they are insensitive to signal to noise ratio （SNR） variation. According to good classification by the correct rate of a neural network classifier, a multilayer perceptron （MLP） classifier with better generalization, as well as, addition of time-frequency features set for classifying six different modulation types has been proposed. Computer simulations show that the MLP classifier outperforms the decision-theoretic classifier at low SNRs, and the classification experiments for real MPSK signals verify engineering significance of the MLP classifier.

DOPPLERLET BASED TIME-FREQUENCY REPRESENTATION VIA MATCHING PURSUITS

A new time-frequency representation called Dopplerlet transform, which uses the dilated, translated and modulated windowed Doppler signals as its basis functions, is proposed, and the Fourier transform, short-time Fourier transform (including Gabor transform), wavelet transform, and chirplet transform are formulated in one framework of Dopplerlet transform accordingly.It is proved that the matching pursuits based on Dopplerlet basis functions are convergent, and that the energy of residual signals yielded in the decomposition process decays exponentially. Simulation results show that the matching pursuits with Dopplerlet basis functions can characterize compactly a nonstationary signal.

Joint Time-Frequency Analysis of Seismic Signals:A Critical Review

This paper presents an evaluation of time-frequency methods for the analysis of seismic signals.Background of the present work is to describe,how the frequency content of the signal is changing in time.The theoretical basis of short time Fourier transform,Gabor transform,wavelet transform,S-transform,Wigner distribution,Wigner-Ville distribution,Pseudo Wigner-Ville distribution,Smoothed Pseudo Wigner-Ville distribution,Choi-William distribution,Born-Jordan Distribution and cone shape distribution are presented.The strengths and weaknesses of each technique are verified by applying them to a particular synthetic seismic signal and recorded real time earthquake data.

NON-STATIONARY SIGNAL DENOISING USING TIME-FREQUENCY CURVE SURFACE FITTING

Based on the theory of adaptive time-frequency decomposition and Time-Frequency Dis- tribution Series (TFDS), this paper presents a novel denoising method for non-stationary signal. Ac- cording to the input signal features, an appropriate kind of elementary functions with great concen- tration in the Time-Frequency (TF) plane is selected. Then the input signal is decomposed into a linear combination of these functions. The elementary function parameters are determined by using ele- mentary function TF curve surface to fit the input signal’s TFDS. The process of curved surface fitting corresponds to the signal structure matching process. The input signal’s dominating component whose structure has the resemblance with elementary function is fitted out firstly. Repeating the fitting process, the residue can be regarded as noises, which are greatly different from the function. Selecting the functions fitted out initially for reconstruction, the denoised signal is obtained. The performance of the proposed method is assessed by means of several tests on an emulated signal and a gearbox vi- brating signal.

The 0 ,1 - Distribution of the First CoordinateSequences Derived from ML- Sequences over Z/(2~e)

The 0,1 distribution of the first coordinate sequences derived from the maximal lenght sequences (ML sequences) over Z/(2~e) is exactly given.

ESMD Method for Frequency Distribution of Tank Surface Temperature under Wind Effect

Due to the poor understanding of the small-scale processes at the air-water interface, some lab experiments are done in a water tank by infrared techniques. With the help of ESMD method, the stochastic temperature sequences extracted from the infrared photographs are decomposed into several empirical modes of general periodic forms. The corresponding analyses on the modes reveal that, within certain limits, both spatial and temporal frequencies increase along the wind speed. As for the amplitudes, the existence of wind may result in fold increasing of their values. In addition, when the wind speed is added from 4 m/s to 5 m/s, both frequency and amplitude of the surface temperature decrease and it implies an enhanced mixing and a weakened temperature gradient under the force of wind blowing.