Wigner-Ville Distribution Research Articles

Efficient Rotational Angular Velocity Estimation of Rotor Target via Modified Short-Time Fractional Fourier Transform

As a special micro-motion feature of rotor target, rotational angular velocity can provide a discriminant basis for target classification and recognition. In this paper, the authors focus on an efficient rotational angular velocity estimation method of the rotor target is based on the combination of the time–frequency analysis algorithm and Hough transform. In order to avoid the problems of low time–frequency resolution and cross-term interference in short-time Fourier transform and Wigner–Ville distribution algorithm, a modified short-time fractional Fourier transform (M-STFRFT) is proposed to obtain the time-FRFT domain (FRFD)-frequency spectrum with the highest time–FRFD–frequency resolution. In particular, an orthogonal matching pursuit (OMP)-based algorithm is proposed to reduce the computational complexity when estimating the matched transform order in the proposed M-STFRFT algorithm. Firstly, partial transform order candidates are selected randomly from the complete candidates. Then, a partial entropy vector corresponding to partial transform order candidates is calculated from the FRFT results and utilized to reconstruct the complete entropy vector via the OMP algorithm, and the matched transform order can be estimated by searching minimum entropy. Based on the estimated matched transform order, STFRFT is performed to obtain the time–FRFD–frequency spectrum. Moreover, Hough transform is employed to obtain the energy accumulation spectrum, and the micro-Doppler parameter of rotational angular velocity can be estimated by searching the peak value from the energy accumulation spectrum. Both simulated data and measured data collected by frequency modulated continuous wave radar validate the effectiveness of the proposed algorithm.

Automated defect identification from carrier fringe patterns using Wigner-Ville distribution and a machine learning-based method.

The paper presents a method for automated defect identification from fringe patterns. The method relies on computing the fringe signal's Wigner-Ville distribution followed by a supervised machine learning algorithm. Our machine learning approach enables robust detection of fringe pattern defects of varied shapes and alleviates the limitations associated with thresholding-based techniques that require careful control of the threshold parameter. The potential of the proposed method is demonstrated via numerical simulations to identify different types of defect patterns at various noise levels. In addition, the practical applicability of the method is validated by experimental results.

Analysis of fractality and complexity of the planetary K-index

The objective of this research is to explore the inherent complexities and multifractal properties of the underlying distributions in the daily Planetary K-index time series collected from NOAA Space Weather Prediction Center. In this article, non-stationary and nonlinear characteristics of the signal have been explored using Smoothed Pseudo Wigner–Ville Distribution and Delay Vector Variance algorithms, respectively, while Recurrence Plot, 0–1 test, Recurrence Quantification Analysis and correlation dimension analysis have been applied to confirm and measure the chaos in the signal under consideration. Multifractal detrending moving average has been used to evaluate the multifractality and also recognise the singularities of the signal. The result of these analyses validates the nonstationary and nonlinear characteristics of the Planetary K-index signal, while a significant presence of deterministic chaos in it has also been noticed. It has also been confirmed that the Planetary K-index exhibits multifractal nature with positive persistence. The long-range temporal association and also the large pdf are discovered to be the primary factors that contribute to the multifractal behaviour of the Kp-index.

Motion Parameters Estimation of a Moving Target Based on Instantaneous Frequency Estimates Using a Passive Acoustic Sensor

This paper studies a method for estimating the motion parameters [Formula: see text] using the instantaneous frequency estimates of the acoustical signal emitted from a moving target in the air and received by an acoustic sensor placed on the ground. Here, [Formula: see text] is the target’s travel speed, [Formula: see text] is the closest point of approach slant range, [Formula: see text] is the source acoustical frequency, and [Formula: see text] is the time at the target get to the closest point of approach to the sensor. A novel relationship formula between the instantaneous frequency and motion parameters is derived and an algorithm for estimating the motion parameters based on the solution of quadratic nonlinear optimization from the instantaneous frequency estimates is proposed. The instantaneous frequency is estimated by searching the peak of a polynomial Wigner–Ville distribution. An approach for calculating the optimal window width in a polynomial Wigner–Ville distribution is proposed. Numerical examples are provided for validating our theoretic claims.

Application research on the time–frequency analysis method in the quality detection of ultrasonic wire bonding

Imperfection in a bonding point can affect the quality of an entire integrated circuit. Therefore, a time–frequency analysis method was proposed to detect and identify fault bonds. First, the bonding voltage and current signals were acquired from the ultrasonic generator. Second, with Wigner–Ville distribution and empirical mode decomposition methods, the features of bonding electrical signals were extracted. Then, the principal component analysis method was further used for feature selection. Finally, an artificial neural network was built to recognize and detect the quality of ultrasonic wire bonding. The results showed that the average recognition accuracy of Wigner–Ville distribution and empirical mode decomposition was 78% and 93%, respectively. The recognition accuracy of empirical mode decomposition is obviously higher than that of the Wigner–Ville distribution method. In general, using the time–frequency analysis method to classify and identify the fault bonds improved the quality of the wire-bonding products.

Application of the joint algorithm of smooth pseudo Wigner-Ville distribution and four-parameter particle swarm optimization to BOTDR

Short-time Fourier transform is utilized for the data processing of traditional point-frequency Brillouin optical time-domain reflectometry (BOTDR). This method can improve the measurement speed, but theoretically there is a contradiction between spatial resolution and frequency resolution. To avoid this contradiction, a joint algorithm of smooth pseudo Wigner-Ville distribution (SPWVD) and four-parameter particle swarm optimization (four-parameter PSO) algorithm is proposed to improve spatial resolution, frequency resolution and frequency shift extraction accuracy of Brillouin scattering spectrum. SPWVD can smooth the signal to enhance the frequency resolution by adding a sliding window on time and frequency domain simultaneously when making the quadratic time-frequency transforming. To further improve the fit and the extraction accuracy of the frequency shift, the Brillouin scattering spectra (BSS) processed by SPWVD are fitted to find the Brillouin frequency shift (BFS) using a four-parameter PSO algorithm that takes the gain, BFS, full width at half maximum of the BSS, and linear weight coefficients of Lorentz and Gaussian lines as unknown parameters. According to the experimental results, the BOTDR using SPWVD and four-parameter PSO joint algorithm will cost less operation time since it can get better results with fewer accumulations and it does not need to find proper initial values before curve-fitting operation. Meanwhile, the joint algorithm can improve the spatial resolution and frequency resolution over four and two times simultaneously for BOTDR with 100 ns pump pulse width.

A fused-image-based approach to detect obstructive sleep apnea using a single-lead ECG and a 2D convolutional neural network.

Obstructive sleep apnea (OSA) is a common chronic sleep disorder that disrupts breathing during sleep and is associated with many other medical conditions, including hypertension, coronary heart disease, and depression. Clinically, the standard for diagnosing OSA involves nocturnal polysomnography (PSG). However, this requires expert human intervention and considerable time, which limits the availability of OSA diagnosis in public health sectors. Therefore, electrocardiogram (ECG)-based methods for OSA detection have been proposed to automate the polysomnography procedure and reduce its discomfort. So far, most of the proposed approaches rely on feature engineering, which calls for advanced expert knowledge and experience. This paper proposes a novel fused-image-based technique that detects OSA using only a single-lead ECG signal. In the proposed approach, a convolutional neural network extracts features automatically from images created with one-minute ECG segments. The proposed network comprises 37 layers, including four residual blocks, a dense layer, a dropout layer, and a soft-max layer. In this study, three time–frequency representations, namely the scalogram, the spectrogram, and the Wigner–Ville distribution, were used to investigate the effectiveness of the fused-image-based approach. We found that blending scalogram and spectrogram images further improved the system’s discriminative characteristics. Seventy ECG recordings from the PhysioNet Apnea-ECG database were used to train and evaluate the proposed model using 10-fold cross validation. The results of this study demonstrated that the proposed classifier can perform OSA detection with an average accuracy, recall, and specificity of 92.4%, 92.3%, and 92.6%, respectively, for the fused spectral images.

A Blind Parameter Estimation Method of Frequency Hopping Signal with Low SNR

In order to effectively estimate the parameters of the frequency hopping signals under low signal-to-noise ratio (SNR), a blind parameter estimation method based on the modified discrete time Wigner-Ville distribution (MDTWVD) is proposed. We choose a low order Chebyshev polynomial as the kernel function for reducing the cross-term. Then, the parameters of the frequency hopping signals are finally obtained from the MDTWVD. The simulation experiment results show that the method used in this paper can effectively and accurately estimate frequency hopping signals parameters, especially under low SNR condition compared with other estimating methods.

Seismic Signal Filtering based on Pseudo Wigner-Ville Distribution and Catte Model

In practice, there are various noises included in the collected seismic data. As a common background noise, random noise may interfere even annihilate valid signals. In view of this, it needs to adopt effective methods to eliminate random noise as much as possible. This paper proposes a filtering method that is based on pseudo Wigner-Ville distribution (PWVD) and Catte model. PWVD is a windowed form of Wigner-Ville distribution (WVD) which can make the nonlinear signal to be locally linearized in addition to weakening the influence of cross item. And the Catte model is a kind of anisotropic diffusion algorithm which can eliminate the noise while protecting the edge of image. The implementation of the proposed method is to do PWVD for the frequency modulation form of noise-containing signal and then to filter the PWVD via Catte model, at last to adopt peak search to obtain the estimation of the valid signal.

Incipient Surge Detection in Large Volume Energy Systems Based on Wigner–Ville Distribution Evaluated on Vibration Signals

Abstract Compressor response investigation in nearly unstable operating conditions, like rotating stall and incipient surge, is a challenging topic nowadays in the turbomachinery research field. Indeed, turbines connected with large-size volumes are affected by critical issues related to surge prevention, particularly during transient operations. Advanced signal-processing operations conducted on vibrational responses provide an insight into possible diagnostic and predictive solutions which can be derived from accelerometer measurements. Indeed, vibrational investigation is largely employed in rotating-machine diagnostics together with time-frequency analysis such as smoothed pseudo-Wigner Ville (SPWVD) time-frequency distribution (TFD) considered in this paper. It is characterized by excellent time and frequency resolutions and thus it is effectively employed in numerous applications in the condition monitoring of machinery. The aim and the innovation of this work regards SPWVD utilization to study turbomachinery behavior in detail in order to identify incipient surge conditions in the centrifugal compressor starting from operational vibrational responses measured at significant plant locations. The so developed investigation allows us to assess the reliability of this innovative technique with respect to conventional ones in this field of research, highlighting at the same time its qualities and drawbacks in detecting fluid machinery unstable behavior. To this aim, an experimental campaign has been conducted on a T100 microturbine connected with several volume sizes and this has allowed to assess diagnostic technique reliability in plant configurations with different dynamic properties. The results show that SPWVD is able to successfully identify system evolution toward an unstable condition, by recognizing different levels and features of the particular kind of instability that is going to take place within the plant. Instability phenomena regarding rolling bearings have also been identified and their interaction with surge onset has been investigated for diagnostic purposes.

Single-pixel holographic rod-shaped particle sizing without depth search using Wigner-Ville distribution

Digital holographic measurement of rod-shaped particle size from inline holograms using a single-pixel of Wigner-Ville distribution (WVD) coefficients is proposed. The proposed sizing method detects only the spatial frequency coordinate of the single WVD output coefficient with a minimum amplitude to measure the particle size. The proposed method has advantages over conventional numerical reconstructions in that iterative and time-consuming particle depth searches are obviated. Besides its faster response, its sizing accuracy is higher than the angular spectrum method and the previous WVD-based method because it is free from errors in depth-search. The proposed method is experimentally verified by using microtube objects with different diameters.

A New GNSS Interference Detection Method Based on Rearranged Wavelet-Hough Transform.

Since radio frequency interference (RFI) seriously degrades the performance of a global navigation satellite system (GNSS) receiver, interference detection becomes very important for GNSS receivers. In this paper, a novel rearranged wavelet–Hough transform (RWHT) method is proposed in GNSS interference detection, which is obtained by the combination of rearranged wavelet transform and Hough transform (HT). The proposed RWHT method is tested for detecting sweep interference and continuous wave (CW) interference, the major types of GNSS interfering signals generated by a GNSS jammer in a controlled test bench experiment. The performance of the proposed RWHT method is compared with the conventional techniques such as Wigner–Ville distribution (WVD) and Wigner–Hough transform (WHT). The analysis results show that the proposed RWHT method reduces the influence of cross-item problem and improves the energy aggregation property in GNSS interference detection. When compared with the WHT approach, this proposed RWHT method presents about 90.3% and 30.8% performance improvement in the initial frequency and chirp rate estimation of the GNSS sweep interfering signal, respectively. These results can be further considered to be the proof of the validity and effectiveness of the developed GNSS interference detection method using RWHT.

Group Velocity Estimation and Defect Localization in Magneto-Inductive Waveguides

We report on time-frequency analysis (TFA) of dispersion in a 1-D magneto-inductive waveguide (MIW). The short-time Fourier transform (STFT) and Wigner-Ville distribution (WVD) are used to localize the frequency content of the dispersed wave as a function of time and to estimate the group velocity in experiments using a 1-D MIW constructed with planar resonators. Time-domain reflectometry (TDR) measurements are performed after deliberately introducing defects along the waveguide; and the results are analyzed with TFA, demonstrating the potential for using such MIW-TDR configurations as sensors. The WVD-TFA is shown to provide precise time-frequency information, accurate defect localization, and group velocity estimation, confirming the slow wave long-range nature of dispersive MIWs. The adaptability of the MIW-TDR setup and the accuracy of the WVD for localization make the technique a suitable candidate for sensing applications using engineered dispersive media.

Application of the Reassigned Smoothed Pseudo Wigner-Ville Distribution in Gear Defect Diagnosis

Gear is one of the most omnipresent components in the mechanical and industrial fields. Some defects can occur causing a change in the vibration signature. In the dynamic of gears system, several sources of excitation are considered. The principal objective of the present work is to study the use of the Reassigned Smoothed Pseudo Wigner Ville Distribution (RSPWVD) in the gear vibration monitoring. The used signals are obtained by the simulation of an eight degrees of freedom gearbox system for the healthy and cracked case. The considered model takes into account the presence of friction force inter teeth in contact, backlash and time varying mesh stiffness. Also, the presence of noise is highlighted. A comparison with the Smoothed Pseudo Wigner Ville Distribution (SPWVD) is done.

Instantaneous frequency extraction of highly nonstationary optical interferometric signal using Reassigned Smoothed Pseudo Wigner Ville Distribution

Instantaneous frequency (IF) of optical interferometric signal often carries information on various physical parameters such as velocity, strain and displacement. We propose smoothed Pseudo Wigner-Ville distribution method for extracting IF of highly non-stationary polynomial frequency modulated (FM) fringe signal. Cohen class signal representation is followed and time and frequency resolutions are independently optimized using separable kernel. Reassignment technique is further applied for sharpening of the spectrogram with these optimized kernels that improves accuracy in IF significantly. Quadratic FM along with strong nonlinear IF based fringe signal is considered for showing the efficacy of proposed method. Results are compared with that of existing Polynomial Wigner Ville Distribution method and Continuous Wavelet Transform (CWT) based approach and found to be more accurate in proposed technique. Finally fringe signal generated by varying the length of one of the legs of Michelson interferometer has been used to validate the proposed method experimentally.

Internal Combustion Engine Fault Diagnosis Method Based MICEEMD-PWVD

As to multi-signals, the figure of time-frequency distribution becomes difficult to understand due to cross-terms in the Wigner-Ville distribution (WVD). At present time, cross-terms suppression of time-frequency analysis is one of the top interests in signal processing, and more and more research had been put on this topic, but the present research on cross-terms suppression exist conflicting problem that these methods couldn’t suppress the cross-terms while holding high time-frequency resolution. A novel method of cross-terms suppression in the WVD based on Complementary Ensemble Empirical Mode Decomposition (CEEMD) was proposed to solve the above problem. Firstly, multi-component signals were decomposed into intrinsic mode functions (IMFs) which were single component signal by CEEMD; Secondly, the Mutual Information values of IMFS and original signal were calculated to judge and delete the CEEMD false components; Thirdly, these Wigner-Ville distributions of true component of IMFs were computed; Finally, WVDs of each single component signal were added linearly to reconstruct the WVD of original signal. Test on synthetic data shows the effectiveness of the proposed method, which can suppress the cross-terms while holding high time-frequency resolution. Apply MICEEMD - PWVD in internal combustion engine valve clearance fault diagnosis, useTD-2DPCA method to extract MICEEMD-PWVD time-frequency image feature, then classify the characteristic parameters with the nearest neighbor classifier. The results show that the IC Engine Fault Diagnosis Method Based MICEEMD-PWVD and TD-2DPCA can accurately diagnose IC engine valve fault.

Design of an Optimal Piece-Wise Spline Wigner-Ville Distribution for TFD Performance Evaluation and Comparison

This paper proposes a new performance evaluation process for time-frequency distributions (TFD) by designing a reference optimal TFD and novel accuracy and resolution measures. The motivation comes from the need for a TFD performance evaluation method that is objective, capable of quantifying the TFD accuracy and resolution, can determine the performance difference among different TFDs, and suitable for signals with an arbitrary number of components, instantaneous frequency and amplitude. We formulate the proposed optimal TFD, namely the piece-wise spline Wigner-Ville distribution (PW-WVD), by decomposing a standard non-stationary signal model using piece-wise linear frequency modulated (LFM) basis and by exploiting the Wigner-Ville distribution optimality for LFM signals. We compare the designed PW-WVD to conventional optimal TFDs and show that the former is more suitable to serve as a reference for TFD performance evaluation. Using the PW-WVD we derive TFD accuracy and resolution measures, compare them to conventional approaches, and analyze their sensitivity to form a TFD selection criteria. We evaluate the accuracy and resolution of twelve different TFDs and develop precise TFD selection strategies with or without prior information on the signal parameters. Results indicate that the compact kernel distribution is the best performing TFD given no prior information on the signal parameters and different TFDs must be selected upon the availability of prior information.

A Double-Terminal Traveling-Wave-Based Method Using Novel Noncontact Sensors for Fault Location in Transmission Cable Lines

The burgeoning demand for enhanced power-system safety means that there is increased attention on technologies for the detection and location of cable faults. The double-terminal fault location method, which senses a fault current using a current transformer (CT), is the most effective and widely applied method in industrial practice. However, CT sensors may suffer from magnetic saturation when exposed to a high fault current, resulting in significant location errors, and their sensitivity cannot be adjusted. To address this problem, this paper describes an improved method for the acquisition of fault signal and the identification of fault-wave arrival time in power cables. First, a novel noncontact sensor (NCS) is developed for the detection of electric fields, and its sensitivity-adjustment curves are obtained by theoretical calculation and simulation. Then, based on feedback variational mode decomposition (FVMD) and the Wigner-Ville distribution (WVD), an improved method (the FVMD + WVD method) for the identification of fault-wave arrival time is devised, and its efficacy and accuracy are verified by simulations in Power Systems Computer-Aided Design/Electromagnetic Transients including DC (PSCAD/EMTDC) software. Finally, the fault-wave arrival-time detection performance of the NCS is examined in a series of on-site DC and AC experiments based on damped AC technology. The results show that the NCS exhibits feasible and effective performance, and that its response can be appropriately tuned based on its sensitivity-adjustment curves. The FVMD + WVD method is more accurate than several other current methods, as its error is only 0.48%, and thus this method enables the practical location of cable faults. In sum, these findings demonstrate that the NCS and the FVMD + WVD method comprise an improved system for the detection and location of cable faults, which will enhance cable safety in power systems.

FPGA-Based Wigner–Hough Transform System for Detection and Parameter Extraction of LPI Radar LFMCW Signals

Low probability of intercept (LPI) radars using linear frequency-modulated continuous waveforms (LFMCWs) is rapidly proliferating in the military domain and posing a serious challenge to conventional electronic support receivers (ESRs). In this article, we provide a practical approach that can be used in digital ESR systems for real-time LFMCW radar signal detection and parameter extraction under challenging SNR levels. We proposed a modified version of the Wigner–Ville distribution (WVD), namely, short-time Wigner distribution (STWD), postprocessing steps, e.g., column-based thresholding of STWD combined with the Hough transform (HT), and a field-programmable gate array (FPGA) design as an embedded solution with low computational complexity. The performance of the proposed system is tested with MATLAB and hardware simulations using a signal database generated with different signal-to-noise ratio (SNR) levels. The system is then embedded into a Virtex-7 FPGA where the performance evaluations showed satisfactory detection results down to −6-dB SNR level, and parameter extraction results down to −8-dB SNR level.

Singularity-Exponent-Domain Image Feature Transform.

Combining the generalized fractal theory and the time-frequency distribution, the image feature decomposition in the singularity exponent domain is studied in this paper. With the theoretical derivation and quantitative analysis, the singularity-exponent-domain image feature transform (SIFT) method is proposed to analyze and process images from new feature dimensions. If one derives from the generalized fractal characteristics of the image, the two-dimensional frequency variables of the 2D time-frequency transform of the image can be used to estimate the two-dimensional singularity power spectrum (SPS) in the space dimension. As a consequence, it leads to the SPS distribution of the original image in the spatial domain, i.e., SIFT images. Based on the SIFT, the feature transform images with different singularity exponent and feature curves of singularity power spectrum with respect to different physical regions can thus be obtained. The SIFT is rigorously derived from the 2D-SPS and the Pseudo Wigner-Ville distribution (PWVD). In addition, the feature images based on the SIFT is proved to be the SNR independence in the GWN background. In order to validate the effectiveness of feature extraction, the proposed methodology is tested on the breast ultrasound images, the visual images, and the synthetic aperture radar (SAR) images. Furthermore, the SAR target detection method based on the SIFT images is proposed, and the experiment results indicate that the proposed algorithm is superior in performance to the traditional CFAR or 2D-SPS method. In fact, this new SIFT is promising to provide a technical approach for image feature extraction, target detection, and recognition.