Wigner-Ville Distribution Research Articles

Multiple Frequency Tracking and Mitigation Based on RSPWVD and Adaptive Multiple Linear Kalman Notch Filter

In this paper, the multiple frequency tracking and mitigation method based on the reassigned smoothed pseudo Wigner-Ville distribution (RSPWVD) and an adaptive multiple linear Kalman notch filter (AMLKNF) is proposed to track and mitigate multiple global positioning system (GPS) interference signals. Compared to the conventional notch filters, the AMLKNF has a faster convergence rate and smaller signal loss. However, for using this method, we need to know the notch frequency which is the interference frequency to remove. Thus, we use the RSPWVD method, one of the time-frequency analysis methods. In addition, an adaptation logic is designed in the AMLKNF to adjust the notch depth according to the power of the jamming signal. Matlab-based simulations are performed for analyzing the performance of the proposed method. The simulation results show that the proposed algorithm can efficiently track and eliminate interference well compared to the conventional methods.

Multichannel maximum-entropy method for the Wigner-Ville distribution

The Wigner-Ville distribution is a powerful technique for the time-frequency spectral analysis of nonstationary seismic data. However, the Wigner-Ville distribution suffers from cross-term interference between different wave components in seismic data. To mitigate cross-term interference, we have developed a multichannel maximum-entropy method (MEM) to modify the Wigner-Ville kernel. The method is related to the conventional maximum-entropy spectral analysis (MESA) algorithm because both algorithms use Burg’s reflection coefficients for the calculation of the prediction-error filter (PEF). The MESA algorithm works on the standard autocorrelation sequence, but it does not work for the Wigner-Ville kernel, which is an instantaneous autocorrelation sequence. Our multichannel MEM algorithm uses the PEF to modify any single Wigner-Ville kernel sequence by exploiting multiple Wigner-Ville kernel sequences simultaneously. This multichannel implementation is capable of robustly determining the reflection coefficient and a minimum-phased PEF for the Wigner-Ville kernel sequence. The Wigner-Ville distribution and the multichannel MEM algorithm in conjunction with each other in turn can produce a high-resolution time-frequency spectrum by mitigating the cross-term interferences and suppressing the spurious energy in the spectrum.

Estimation of time-parameters of Barker binary phase coded radar signal using instantaneous power based methods

This paper deals with analysis of the Barker binary phase radar signal as part of ways to counteract upcoming threats in the field of electronic warfare support (ES) system. The ES part of electronic warfare (EW) provides tactical support by providing key information to other sections responsible for providing response in the form of attack and protection. The analysis of this paper focused on the correct estimation of the basic time parameters (pulse width and pulse repetition period) of this radar signal using instantaneous power obtained from the time-marginal of the time-frequency distribution (TFD), the maxima (power) of the TFD and directly from the product of signal. The main TFD is a modified version of the most common quadratic TFD (QTFD), the Wigner-Ville distribution (WVD) using appropriately chosen separable kernels. This analysis and estimation method developed is tested in the presence of white noise of Gaussian probability density function at different signal-to-noise ratios (SNR). Results obtained show that instantaneous power gotten from the maxima of TFD outshines the other methods with a minimum SNR of?14 dB when the specific threshold of 37.5% is used. It also shows that the proposed methods chosen outperform previous works of similar objectives and therefore, making it suitable for practical EW systems.

Tomographic and entropic analysis of modulated signals-=SUP=-*-=/SUP=-

We study an application of the quantum tomography framework for the time-frequency analysis of modulated signals. In particular, we calculate optical tomographic representations and Wigner-Ville distributions for signals with amplitude and frequency modulations. We also consider time-frequency entropic relations for modulated signals, which are naturally associated with the Fourier analysis. A numerical toolbox for calculating optical time-frequency tomograms based on pseudo Wigner-Ville distributions for modulated signals is provided.

Parameter Optimization of Generalized S Transform Based on Improved Genetic Algorithm

Background: For the traditional Fourier Transform (FT), it cannot effectively detect the frequency of non-stationary signals with time. Analyzing the local characteristics of time-varying signal by using FT is hard to achieve. Therefore, many time-frequency analysis methods which can meet different needs have been proposed on the basis of the traditional Fourier transform, like the Short Time Fourier Transform (STFT), the widely used Continuous Wavelet Transform (CWT), Wigner-Ville Distribution (WVD) and so on. However, the best time and frequency resolution cannot be achieved at the same time due to the uncertainty criterion. Methods: From the point of view of optimizing time-frequency performance, a new Generalized S Transform (GST) window function optimization method is proposed by combining time frequency aggregation with an improved genetic algorithm in this paper. Results: In the noiseless condition, the Linear Frequency Modulation (LFM), Nonlinear Frequency Modulation (NLFM) and binary Frequency Shift Keying (2FSK) signals are simulated. The simulation results prove that the method can improve the time-frequency concentration and decreasing Rényi entropy effectively. Compared with other four traditional time-frequency analysis methods, the improved GST has more advantages. Conclusion: In this paper, a new method of optimizing the window function in GST based on improved GA is proposed in this paper. Experiments on LFM, NLFM and 2FSK signals show that the proposed method not only has the advantages of high resolution, but also determines the optimal parameters via the time frequency focusing criterion and the Rényi entropy. Compared with the other four kinds of time-frequency analysis methods, the optimized GST based on improved GA in this paper has the best time-frequency focusing.

Quantum bridges in phase space: interference and nonclassicality in strong-field enhanced ionisation

We perform a phase-space analysis of strong-field enhanced ionisation in molecules, with emphasis on quantum-interference effects. Using Wigner quasi-probability distributions and the quantum Liouville equation, we show that the momentum gates reported in a previous publication (Takemoto and Becker 2011 Phys. Rev. A 84 023401) may occur for static driving fields, and even for no external field at all. Their primary cause is an interference-induced bridging mechanism that occurs if both wells in the molecule are populated. In the phase-space regions for which quantum bridges occur, the Wigner functions perform a clockwise rotation whose period is intrinsic to the molecule. This evolution is essentially non-classical and non-adiabatic, as it does not follow equienergy curves or field gradients. Quasi-probability transfer via quantum bridges is favoured if the electron’s initial state is either spatially delocalised, or situated at the upfield molecular well. Enhanced ionisation results from the interplay of this cyclic motion, adiabatic tunnel ionisation and population trapping. Optimal conditions require minimising population trapping and using the bridging mechanism to feed into ionisation pathways along the field gradient.

The Wigner-Ville Distribution Associated with the Quaternion Offset Linear Canonical Transform

The Wigner-Ville distribution (WVD) and the quaternion offset linear canonical transform (QOLCT) are useful tools in signal analysis and image processing. The purpose of this paper is to define the Wigner-Ville distribution associated with the quaternionic offset linear canonical transform (WVD-QOLCT). Actually, this transform combines both the results and flexibility of the two transforms WVD and QOLCT. We derive some important properties of this transform such as inversion and Plancherel formulas, we establish a version of the Heisenberg inequality, Lieb’s theorem and we give the Poisson summation formula for the WVD-QOLCT.

K-SVD-based WVD enhancement algorithm for planetary gearbox fault diagnosis under a CNN framework

This paper presents a new method of planetary gearbox fault diagnosis by dealing with and analyzing vibration signals. This study contributes to the realization of automatic diagnosis using a convolution neural network (CNN) to process time-frequency distributions (TFDs) transformed from vibration time series. In order to solve the problem of non-stationary working states and strong noise interference in industrial applications, a K-singular value decomposition (K-SVD) is used to enhance the resolution of TFDs obtained by Wigner–Ville distribution (WVD), a typical time-frequency transform algorithm. The simulation results indicate that K-SVD can not only reduce the effects of cross-terms on WVDs but can also eliminate noise, which makes the fault characteristics outstanding in the time-frequency domain. The enhanced WVDs improve the accuracy of fault diagnosis in a classification framework based on the CNN that can extract features adaptively and obtain a high degree of discrimination between different fault conditions. Finally, the effectiveness of the proposed method is verified by a prototype experiment with roller bearings and a scale test rig of a planetary gearbox from a ship unloader. Moreover, a priority confusion matrix is proposed as a visualization tool with which to evaluate the performance of a fault diagnosis model. The results open the possibility of extrapolating the method to the fault diagnosis of other mechanical parts.

Vibration Analysis of a Rotating Flywheel/Flexible Coupling System with Angular Misalignment and Rubbing Using Smoothed Pseudo Wigner–Ville Distributions

Detection of early faults such as misalignment, rotor rubbing, shaft crack and bearing fault is necessary to avoid harmful and even catastrophic influences on rotating machinery. In this paper, the accelerating horizontal and pitching vibration responses of flywheel/flexible coupling model of an actual diesel generator, with angular misalignment and rubbing faults, are investigated using the smoothed pseudo-Wigner–Ville distributions (SPWVDs). Numerical simulations are performed through the dynamical equations of the flywheel/flexible coupling system; the results suggest that when an angular misalignment fault occurs, the super-harmonic resonance of order 3 can be found in the horizontal and pitching vibration signals. Meanwhile, both the 3fr and 5fr components (i.e., 3 and 5 times of the rotating frequencies) can also be found in SPWV distribution spectra. When rubbing fault occurs, more abundant sub- and super-harmonic frequency components can be observed in SPWV distribution spectra. Overall, the investigation shows that the smoothed pseudo-Wigner–Ville distribution spectra reveal obvious differences between the acceleration responses of the rotating system with different faults.

Spectral Decomposition of Seismic Data With Variational Mode Decomposition-Based Wigner–Ville Distribution

Wigner–Ville distributions (WVDs), which provide superior time-frequency resolution and energy distribution concentration relative to other traditional Fourier-based or wavelet-based seismic time-frequency methods, are an important tool for spectral decomposition and have the potential to yield better seismic interpretations for highlighting geophysical responses in particular frequency bands. However, the existence of cross-term interference in WVDs limits their application. To effectively suppress the cross-term interference in a WVD without reducing the time-frequency resolution and energy aggregation, we propose a variational mode decomposition (VMD) based WVD approach. VMD is first used to decompose the multicomponent seismic data into a series of narrow band limited intrinsic mode functions (IMFs). Next, we calculate the WVDs of these IMFs. Finally, the maximum amplitude volume above the average amplitude and the peak frequency volume are extracted from these WVDs for seismic interpretation. A synthetic data example demonstrates the effectiveness of the VMD-based WVD approach and its superiority comparison to the WVD, smoothed pseudoWVD and empirical mode decomposition based WVD approaches. Real seismic data applications show that spectral decomposition with VMD-based WVD has a strong ability to highlight hydrocarbon-related information.

Detection and Line Selection of Series Arc Fault in Multi-Load Circuit

In order to study a kind of detection and line selection method of arc fault in actual power supply and distribution lines, arc fault experiments with multi-load loop were carried out. First, five-layer decomposition of main loop current was made by using wavelet packet. The effective coefficients were selected based on the change rate of a wavelet packet energy entropy before and after the arc fault occurs. Then, an effective signal of the arc fault was reconstructed. Second, the effective signal was decomposed into seven independent modes with a variational mode decomposition method. Its time–frequency distribution was obtained by solving the Wigner–Ville distribution and performing a linear summation of each mode. Third, the time-domain and time–frequency features of arc fault were extracted by analyzing the time-domain waveform and time–frequency distribution of the effective signal. An arc fault identification and line-selection model was established by using a support vector machine optimized by particle swarm optimization and grid search. Then, the accuracy of both arc fault detection and line selection were tested. Test results indicated that the proposed method can detect effectively arc fault and select fault line accurately.

Detecting instant of multiple faults on the transmission line and its types using time–frequency analysis

In a complex interconnected network, due to dynamic interaction between the AC networks, during occurrences of faults, the successful relay operation is threatened. For security and reliability of the power system network, a fast and accurate protection scheme is of great importance. This study presents a protection scheme for multiple fault detection at bus/line and its type in a wide area network. If a fault occurs on a line, followed by another fault at the same/different line, before the clearance of former fault, the proposed scheme is capable of detecting such multiple fault events. The scheme applies processed signal information for its time–frequency representation using Smoothed Pseudo Wigner–Ville distribution, followed by Hilbert transform and calculation of indices to interpret the fault events. It is shown that faulted bus, faulted line, time instant, and types of faults can be easily identified with low computational burden. The scheme is validated on the signals simulated on Kundur's model, IEEE 39 bus system and verified with signals on real-time digital simulator for different fault conditions; fault resistance and fault location on the line. The scheme can be successfully applied on signals available from phasor measurement units for wide area network protection.

State-independent quantum state tomography by photon-number-resolving measurements

The Wigner quasiprobability distribution of a narrowband single-photon state was reconstructed by quantum state tomography using photon-number-resolving measurements with transition-edge sensors (TES) at system efficiency 58(2)%. This method makes no assumptions on the nature of the measured state, save for the limitation on photon flux imposed by the TES. Negativity of the Wigner function was observed in the raw data without any inference or correction for decoherence.

Random noise suppression of seismic data by time–frequency peak filtering with variational mode decomposition

Random noise suppression is of great importance in seismic processing and interpretation, and time–frequency peak filtering (TFPF) is a classic denoising approach. In TFPF, pseudo Wigner–Ville distribution (PWVD) is used to linearise the given signal for an unbiased estimation of the instantaneous frequency. However, window length is a trade-off parameter for preserving valid signals and attenuating random noise. A long window length may cause loss of the desired signal, whereas a short window length may be inadequate to suppress noise. To ensure a good trade-off between signal preservation and noise reduction, empirical mode decomposition (EMD) has been introduced into the TFPF method. Although the EMD-TFPF method can achieve good results, the mode mixing problem in EMD is non-negligible. In this article, we introduce variational mode decomposition (VMD) to overcome the mode mixing problem. VMD decomposes a signal into an ensemble of modes that own their respective centre frequencies. Thus, the modes obtained by VMD contain less noise, which simplifies selection of the window width of TFPF. Therefore, we propose the VMD-based TFPF (VMD-TFPF) method to suppress random noise. Synthetic and field seismic data examples are employed to illustrate the superior performance of the proposed method in attenuating random noise and preserving the desired signal.

Time–Frequency-Based Condition Monitoring of 22.9-kV HTS Cable Systems: Cooling Process and Current Imbalance

In this paper, new time–frequency-based anomaly detection methodology is proposed for the condition monitoring of high-temperature superconducting (HTS) cable systems. The time–frequency-based anomaly detection methodology includes two indices, which are obtained via cross Wigner–Ville distribution and scattering parameter. For the validation of the proposed methodology, the methodology is applied to an ac 22.9-kV/50-MVA HTS cable system connected to the real power grid network. Furthermore, the changes in dielectric properties of the HTS cable system during the cooling process and the current imbalance failure are monitored. The proposed anomaly detection indices are shown to be able to detect the heat and the current imbalance caused by the malfunction of the joint box. For the application of the two validated indices, new anomaly detection procedure for HTS cable systems is also presented.

Target detection in pseudo Wigner-Ville distribution of underwater beamformed signals

Because of clutter or reverberation in the water, it is difficult to distinguish a target from them with a beamforming image. It is well-known that the pseudo Wigner-Ville distribution, which is high-resolution time-frequency processing, can detect target signals effectively. In this study, the pseudo Wigner-Ville distribution with the beamformed signals was analyzed to detect an underwater target. The acoustic signals were measured using an array system consisting of a transmitting transducer and a line array of 16 elements at sea. The target was an air-filled aluminum spherical shell with a thin thickness. The transmitted signal was 3 to 8 kHz linear frequency modulation continuous waveforms. The experiment results show that the target can be easily identified with the pseudo Wigner-Ville distribution. [Work financially supported by the research project PES3180 funded by KRISO.]

Intelligent Noise Elimination Algorithm for Marine Communication Based on Cluster Collaboration

Wang, X.; Fang, D.; Wan, S., and Cheng, Y., 2019. Intelligent noise elimination algorithm for marine communication based on cluster collaboration In: Guido-Aldana, P.A. and Mulahasan, S. (eds.), Advances in Water Resources and Exploration. Journal of Coastal Research, Special Issue No. 93, pp. 753–761. Coconut Creek (Florida), ISSN 0749-0208.In order to overcome the large amount of noise in marine communication and further improve the quality of communication under low SNR, an intelligent noise elimination algorithm based on cluster cooperation is proposed. Firstly, a finite perception congestion model is established, and a noise control strategy based on denoising operator for consistency algorithm is proposed. It is pointed out that when ε (t) is a high order infinite, the consistency algorithm after denoising can control the noise, make the Agent to converge to the original convergence state, and make the center to distribute normally. By frequency modulation, the noisy signal in communication is modulated into the instantaneous frequency of the analytic signal. In view of the non-linear characteristics of the marine communication signal, the cluster collaboration algorithm is realized by using the windowed Wigner-Ville distribution. For the high noise situation, the iterative algorithm can be used until the noise is completely eliminated. Experiments show that the algorithm can effectively eliminate communication noise and has high real-time performance.

Time-frequency analysis of non-stationary neutron noise in a small modular nuclear reactor

In this work, for the first time, the time-frequency analysis technique is proposed to analyze a non-stationary neutron noise. The work investigates on an appropriate way to solve the neutron noise equation in the time-frequency domain in an SMR reactor. To actualize this procedure, a computer program has been developed. This program is based on the use of three main modules. The first is a static calculation by a finite difference method and a power iteration algorithm for providing a database of the required neutronic parameters. The second is the neutron noise calculations in the time-frequency domain and the extraction of the noise characteristics by using the Wigner-Ville distribution. The third is the categorization of the neutron noise sources based on their extracted characteristics such as the source type, the source location, the number of sources, the time of the occurrence, the instance frequency and the noise amplitude.In the first module, the static calculations are benchmarked by the referenced values. Then, in order to validate the static noise calculation, the obtained result is compared to the result of the noise calculation in zero frequency. The results of adjoint and direct methods are compared with each other to confirm the validity of the dynamic noise calculation. The obtained results show a good agreement with each other. In addition, the obtained results of the proposed method and Fourier method are compared with each other at the initial time. Moreover, various noise sources, including mono and multi-frequency, are solved in the time-frequency domain to evaluate the proposed method’s capability.All results show that the proposed method has a good capability to solve neutron noise equation. The results obtained show that the time-frequency method gives comprehensive results in comparison with frequency methods.Finally, it is concluded that analyzing the noise sources in the time-frequency domain can be used as a remarkable approach to investigate the core behavior and to recognize the non-stationary processes in the core.

Analysis of acoustic scattering characteristics of an aluminum spherical shell with different internal fluids and classification using pseudo Wigner-Ville distribution

Analysis of acoustic scattering characteristics of an aluminum spherical shell with different internal fluids and classification using pseudo Wigner-Ville distribution

Time-energy filtering of single electrons in ballistic waveguides

Characterizing distinct electron wave packets is a basic task for solid-state electron quantum optics with applications in quantum metrology and sensing. A important circuit element for this task is a non-stationary potential barrier that enables backscattering of chiral particles depending on their energy and time of arrival. Here we solve the quantum mechanical problem of single-particle scattering by a ballistic constriction in an fully depleted quantum Hall system under spatially uniform but time-dependent electrostatic potential modulation. The result describes electrons distributed in time-energy space according to a modified Wigner quasiprobability distribution and scattered with an energy-dependent transmission probability that characterizes constriction in the absence of modulation. Modification of the incoming Wigner distribution due to external time-dependent potential simplifies in case of linear time-dependence and admits semiclassical interpretation. Our results support a recently proposed and implemented method for measuring time and energy distribution of solitary electrons as a quantum tomography technique, and offer new paths for experimental exploration of on-demand sources of coherent electrons.