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.

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.

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.

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.

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.

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.

Non-Stationary Signal Segmentation and Separation from Joint Time-Frequency Plane

Multi-components sinusoidal engineering signals who are non-stationary signals were considered in this study since their separation and segmentations are of great interests in many engineering fields. In most cases, the segmentation of non-stationary or multi-component signals is conducted in time domain. In this paper, we explore the advantages of applying joint time-frequency (TF) distribution of the multi-component signals to identify their segments. The Spectrogram that is known as Short-Time Fourier Transform (STFT) will be used for obtaining the time-frequency kernel. Time marginal of the computed kernel is optimally used for the signal segmentation. In order to obtain the desirable segmentation, it requires first to improve time marginal of the kernel by using two-dimensional Wiener mask filter applied to the TF kernel to mitigate and suppress non-stationary noise or interference. Additionally, a proper choice of the sliding window and its overlaying has enhanced our scheme to capture the discontinuities corresponding to the boundaries of the candidate segments.

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.

Novel Time-frequency Analysis and Representation of EEG

A novel method of EEG time-frequency analysis and representation based on a wavelet network is presented. The wavelet network model can represent the EEG data effectively. Based on the wavelet network model, a novel time-frequency energy distribution function is obtained, which has the same time-frequency resolution as Wigner-Ville distribution and is free of cross-term interference. There is a great potential for the use of the novel time-frequency representation of nonstationary biosignal based on a wavelet network in the field of the electrophysiological signal processing and time-frequency analysis.

基于改进TFD-Hough变换的时频分量检测

针对通信监测实际环境中现有方法难以有效提取时频分量的问题,提出一种基于改进TFD-Hough变换的时频分量检测算法。在信号分量数目未知的条件下,该方法能充分利用时频分布面各分量的幅值具有线性聚集的特点,通过覆盖聚类和感知编组实现信号分量的逐次提取和参数估计,避免了全局检测中因分量能量差异导致的误检且无法获取目标位置信息的缺陷。实验结果验证了所提方法的有效性,可满足于异常通信信号的主动识别。

Nonexistence of cross-term free time-frequency distribution with concentration of Wigner-Ville distribution

Wigner-Ville distribution (WVD) is recognized as being a powerful tool and a nucleus in time-frequency representation (TFR) which gives an excellent time-frequency concentration, and more importantly, has many desirable properties. A major shortcoming of WVD is the inherent cross-term (CT) interference. Although solutions to this problem from the bulk of contributions to the literature concerning TFR are currently available, none has been able to completely eliminate the CT’s in WVD. It is therefore a common belief that if there exists an auxiliary time-frequency distribution (TFD) which has the same auto-terms (AT’s) as that in WVD, but has CT’s with the opposite sign, then, by adding the auxiliary TFD to WVD, an ideal TFD, which preserves the concentration of WVD while annihilating the CT’s, is readily obtained. However, we prove that the auxiliary TFD does not exist. Moreover, it is found that in general, CT free joint distributions with their concentrations close to that of WVD do not exist either.

基于FTFDS快速重建瞬时ISAR图像

时频分布级数(TFDS)在时频分辨率和交叉项干扰抑制间取得有效平衡,可准确重建复杂机动目标的瞬时ISAR图像。然而原始算法运算效率较低,虽有文献提出了快速计算思路,但难以直接工程应用。文中推导了可直接应用的二维插值滤波器实现形式,在此基础上提出FTFDS算法并从理论与实测两方面分析对比了运算量。分析表明FTFDS明显提升了运算效率,且算法适宜并行计算,时频分析可近实时的实现。仿真数据处理表明,该算法用于瞬时ISAR图像重建快速有效。

Exponential time-frequency distribution of mechanical vibration signals

An improved exponential time-frequency distribution is presented. Compared with those exponential time-frequency distributions represented by the Choi-Williams distribution, this distribution is designed to suit the properties of mechanical vibration signals, and is easier to be applied in the mechanical vibration signal processing. It has a strong cross-term suppression ability and is aliasing free.

Distribution network state estimation based on attention-enhanced recurrent neural network pseudo-measurement modeling

Because there is insufficient measurement data when implementing state estimation in distribution networks,this paper proposes an attention-enhanced recurrent neural network(A-RNN)-based pseudo-measurement modeling metho.First,based on analyzing the power series at the source and load end in the time and frequency domains,a period-dependent extrapolation model is established to characterize the power series in those domains.The complex mapping functions in the model are automatically represented by A-RNNs to obtain an A-RNNs-based period-dependent pseudo-measurement generation model.The distributed dynamic state estimation model of the distribution network is established,and the pseudo-measurement data generated by the model in real time is used as the input of the state estimation model together with the measurement data.The experimental results show that the method proposed can explore in depth the complex sequence characteristics of the measurement data such that the accuracy of the pseudo-measurement data is further improved.The results also show that the state estimation accuracy of a distribution network is very poor when there is a lack of measurement data,but is greatly improved by adding the pseudo-measurement data generated by the model proposed.

基于短时稀疏时频分布的雷达目标微动特征提取及检测方法

为有效提高强杂波及目标复杂运动特性条件下的雷达动目标探测能力,该文结合时频分布(TFD)类动目标检测和稀疏表示方法的优势,建立了短时稀疏TFD(ST-STFD)原理框架,提出短时稀疏傅里叶变换(ST-SFT)和短时稀疏分数阶傅里叶变换(ST-SFRFT)雷达动目标检测方法,并应用于海上目标微动特征提取及检测中。实测雷达数据验证表明,该方法在时间-稀疏域能够实现时变信号的高分辨低复杂度时频表示,具有运算效率高、时频分辨好、抗杂波等优点,为进一步提升雷达杂波抑制和动目标检测能力提供了新的思路和途径。

基于时频形态学滤波的能量积累检测

许多实际应用中,强噪声背景下信号能量的长时间积累是有效检测的关键。该文利用信号在时频平面上的能量聚集特性,提出基于时频域形态学滤波的能量积累检测方法。首先确定时频分布的最优核,计算观测序列的时频分布;然后用阈值处理和形态学滤波估计时频分布的高能量支撑区域;最后累加这些区域的时频能量作为统计量进行检测。仿真结果表明,这种方法在低信噪比下可以有效工作。