Time-frequency Localization Research Articles

Influence of wavelet characteristics on single-phase grounding fault line selection

It is difficult to select the fault line in distribution network because of the small single-phase grounding fault current. Wavelet transform is especially suitable for fault transient analysis because of its unique time-frequency localization performance. However, the characteristics of different wavelets have a direct impact on the line selection results. Improper selection of wavelets will directly lead to misjudgment. Firstly, the transient characteristics of single-phase grounding fault and the relationship between wavelet transform modulus maxima and singularity are analysed, and the line selection criterion of wavelet modulus maxima is given. Then, the influence of wavelet vanishing moment order, support length, symmetry, and orthogonality on the detection effect of signal singularity is analysed, and four principles for selecting wavelet in fault line selection are proposed. The larger the order of vanishing moment and support length, the more conducive to detection. The influence of vanishing moment order is much greater than that of support length. The 10kV system simulation model is built, five representative wavelets are selected to decompose the zero- sequence current of the fault line in four scales respectively, and the different modulus maxima corresponding to the sudden change point are compared. The experimental results prove the reliability of the wavelet selection principles proposed in this paper.

Nonstationary pattern-based signal–noise separation using adaptive prediction-error filter

Abstract Complex field conditions always create different interferences during seismic data acquisition, and there exist several types of noise in the recorded data, which affect the subsequent data processing and interpretation. To separate an effective signal from the noisy data, we adopted a pattern-based method with a two-step strategy, which involves two adaptive prediction-error filters (APEFs) corresponding to a nonstationary data pattern and noise pattern. By introducing shaping regularization, we first constructed a least-squares problem to estimate the filter coefficients of the APEF. Then, we solved another constrained least-square problem corresponding to the pattern-based signal–noise separation, and different pattern operators are adopted to characterize random noise and ground-roll noise. In comparison with traditional denoising methods, such as FXDECON, curvelet transform and local time–frequency (LTF) decomposition, we examined the ability of the proposed method by removing seismic random noise and ground-roll noise in several examples. Synthetic models and field data demonstrate the validity of the strategy for separating nonstationary signal and noise with different patterns.

Seismic Attenuation Estimation via Unscaled Time–Frequency Representation and Divergence

Time-frequency (TF) representations achieve better TF localization properties compared with Fourier transform (FT) and perform well for Q estimation via methods such as spectral ratio (SR), centroid frequency shift (CFS), and peak frequency shift (PFS). However, these attenuation estimation methods all require a given frequency band or certain source wavelet assumptions, also heavily interfered by noise. In addition, the resolution and accuracy of TF spectrum also determine whether the extracted spectrum can accurately characterize the frequency properties of seismic wavelets, thus affecting the accuracy of seismic estimation results. In this study, we propose an unscaled generalized S-transform (UGST), which achieves better TF localization while avoiding the dominant frequency shift of S-transform (ST). Next, we build a Q estimation method based on the weighted Kullback-Leibler (WKL) divergence and then give an estimation workflow combined with the proposed UGST. Note that the proposed workflow does not need to make specific wavelet assumptions or consider the frequency band selection, which is also proved to be not sensitive to noise. Finally, to demonstrate the effectiveness of the proposed workflow, we apply it to synthetic and field data. Compared with the contrastive methods, our proposed workflow can achieve more accurate estimation results and show better noise immunity, which can benefit delineating seismic hydrocarbon reservoirs.

Multi-Synchrosqueezing Wavelet Transform for Time–Frequency Localization of Reservoir Characterization in Seismic Data

Time-frequency analysis (TFA) technology plays a significant role in seismic signal processing. The time-frequency representation (TFR) calculated using the TFA method is helpful for the localization of time-varying frequencies within the signal. Nevertheless, limited by the Heisenberg uncertainty principle, traditional linear TFA methods always provide blurred TFRs, which makes it difficult to distinguish details of time-frequency structures. Recently, the synchrosqueezing transform (SST) was designed to improve the concentration of the TFR. The SST can provide a much concentrated TFR for the weakly frequency-modulated (FM) signal, but it is not effective for the interpretation of strongly FM signals, such as the thin interbed in seismic exploration. In this work, we propose a new tool by introducing the multi-synchrosqueezing operator to the frame of wavelet transform. Employing an iterative operator to correct the frequency estimation of the original SST step-by-step, it thus can calculate a TFR with better concentration and robustness. Synthetic signals and a field seismic data are employed to verify the performance of the proposed method for characterizing the time-varying frequency features.

Norm Estimates for Selfadjoint Toeplitz Operators on the Fock Space

An estimate for the norm of selfadjoint Toeplitz operators with a radial, bounded and integrable symbol is obtained. This emphasizes the fact that the norm of such operator is strictly less than the supremum norm of the symbol. Consequences for time-frequency localization operators are also given.

Geomagnetically Induced Currents: Frequency Spectra and Threats to Voltage Stability

Geomagnetically Induced Currents (GICs) are induced after a complex interaction between the sun and earth’s magnetic field. GICs may cripple power systems leading to voltage collapse and a drop in power quality. While the commonly-used dc model for GICs is valid for steady-state analyses of power systems and transformer responses, GICs must be represented with their continuously varying magnitudes and frequency components to understand the dynamic power system’s response to solar storms. In this paper, we used measured GIC data from the 2003 Halloween storm to compare several signal processing techniques. The Fast Fourier Transform (FFT) with a fixed window size, Short-Time Fourier Transform (STFT) with a variable window size, wavelet transform, and Particle-Swarm Optimization (PSO) methods were used to identify the GIC frequency characteristics. To understand the effects of these GIC characteristics on voltage stability, a multi-machine network was modelled on a digital real-time simulator (OPAL-RT). The results reveal the limitations of fixed window FFT in capturing the dominant high-frequency GIC bandwidth arising during peak solar activity. Wavelet and STFT are recommended for GIC data analysis as they provide time-frequency localization. High-frequency GICs during sudden storm commencements and pulsation activity are more of a concern for voltage stability than lower frequency components. Novel results from this study suggest that limiting contingency analysis to only high magnitudes of dc/GIC does not cater for the underlining GIC dynamics. In addition to magnitude thresholds, contingency analysis should incorporate GIC characteristics such as frequency which affect voltage dynamics and thus power system stability.

Research Progresses of Wavelet Methods and Their Applications in Mechanics

The wavelet theory shows very unique time-frequency localization and multi-resolution analysis ability in signal processing and function approximation. The wavelet basis function has excellent mathematical properties such as orthogonality, compactness, low-pass filtering and interpolation, which endows the wavelet analysis theory with great application potential in the fields of computational mathematics and computational mechanics, and creates new opportunities for breakthrough development in these fields. Since the 1990s, a large number of studies have proved that the numerical method based on the wavelet theory has very obvious advantages in solving differential equations, but at the same time, have exposed some limitations of numerical calculation application caused by the wavelet basis function itself and its unique approximation method. In order to promote the innovative application of the wavelet theory in the fields of computational mathematics and mechanics and provide researchers with a new research perspective, the development background of the wavelet analysis and the research history of methods based on the wavelet theory were reviewed, and the numerical method problems were emphasized and the research progresses made in recent years discussed. The conclusions and comments may provide a meaningful reference for the further development and improvement of quantitative mathematical solution methods based on the wavelet theory and applications in mechanics as well as solutions of a wide range of engineering problems.

Digital Image Watermarking Technique Using Discrete Wavelet Transform and Discrete Cosine Transform

Digital watermarking has been proposed as a viable solution to the need of copyright protection and authentication of multimedia data in a networked environment, since it makes possible to identify the author, owner, distributor or authorized consumer of a document. In this paper a new watermarking technique to add a code to digital images is presented: the method operates in the frequency domain embedding a pseudo-random sequence of real numbers in a selected set of DCT coefficient. And a new method for digital image watermarking which does not require the original image for watermark detection. The watermark is added in select coefficients with significant image energy in the transform domain in order to ensure non- erasability of the watermark. Advantages of the proposed method include: improved resistance to attacks on the watermark, implicit visual masking utilizing the time-frequency localization property of wavelet transform and a robust definition for the threshold which validates the watermark.. Experimental results demonstrate that this proposed technique is robust to most of the signal processing techniques and geometric distortions.

Deep learning analysis for estimating sleep syndromedetection utilizing the twin convolutional model FTC2

Manual sleep stage scoring is frequently performed by sleep specialists by visually evaluating the patient’sneurophysiological signals acquired in sleep laboratories. This is a difficult, time-consuming, and laborious process.Because of the limits of human sleep stage scoring, there is a greater need for creating automatic sleep stageclassification (ASSC) systems. Sleep stage categorization is the process of distinguishing the distinct stagesof sleep and is an important step in assisting physicians in the diagnosis and treatment of associated sleepdisorders. In this research, we offer a unique method and a practical strategy to predict early onset of sleepdisorders, such as restless leg syndrome and insomnia, using the twin convolutional model FTC2, based on analgorithm composed of two modules. To provide localized time-frequency information, 30-second-long epochs ofelectroencephalogram (EEG) recordings are subjected to a fast Fourier transform, and a deep convolutional longshort-term networks neural network is trained for sleep stage categorization. Automating sleep stage detectionfrom EEG data offers a great potential to tackle sleep irregularities on a daily basis. Thereby, a novel approach forsleep stage classification is proposed, which combines the best of signal processing and statistics. In this study,we used the PhysioNet Sleep European Data Format (EDF) database. The code evaluation showed impressiveresults, reaching an accuracy of 90.43, precision of 77.76, recall of 93,32, F1 score of 89.12, and the final meanfalse error loss of 0.09. All the source code is available athttps://github.com/timothy102/eeg..

SparseTFNet: A Physically Informed Autoencoder for Sparse Time–Frequency Analysis of Seismic Data

The time-frequency (TF) analysis is an effective tool in seismic signal processing. The sparsity-based TF transforms have been widely used to obtain high localized TF representations in recent past years. These TF transforms formulate a sparse TF representation as an inverse optimization problem using simple mathematical models, which are typically based on a hand-crafted prior knowledge. Unlike the traditional sparsity-based TF transforms, the supervised deep learning (DL)-based sparse TF representations don’t require this prior knowledge and instead use a large amount of labeled data set, which is difficult to label for seismic data. In this study, to bridge the gap between the traditional sparsity-based transforms and the supervised DL-based transforms, we propose a DL-based sparse TF analysis approach based on a physically informed autoencoder model, named the SparseTFNet. The proposed SparseTFNet includes two modules: a convolutional neural networks (CNN)-based encoder and a traditional inverse TF representation-based decoder. The CNN-based encoder is implemented by training the inverse optimization problem in the absence of the “ground-truth" TF representation, which can be trained with only seismic traces. The traditional inverse short time Fourier transform (STFT) is utilized as the decoder module in this study, which is used as a physical constraint to ensure the high accuracy of the calculated TF representation. Finally, after training and validating the proposed model using the noise-free and noisy synthetic seismic traces, the model is applied to three-dimensional (3D) offshore seismic data. The results show that the proposed SparseTFNet model has good performance in the delineation of the depositional fluvial channels.

Rapid identification of strongly lensed gravitational-wave events with machine learning

A small fraction of the gravitational-wave (GW) signals that will be detected by second and third generation detectors are expected to be strongly lensed by galaxies and clusters, producing multiple observable copies. While optimal Bayesian model selection methods are developed to identify lensed signals, processing tens of thousands (billions) of possible pairs of events detected with second (third) generation detectors is both computationally intensive and time consuming. To mitigate this problem, we propose to use machine learning to rapidly rule out a vast majority of candidate lensed pairs. As a proof of principle, we simulate non-spinning binary black hole events added to Gaussian noise, and train the machine on their time-frequency maps (Q-transforms) and localisation skymaps (using Bayestar), both of which can be generated in seconds. We show that the trained machine is able to accurately identify lensed pairs with efficiencies comparable to existing Bayesian methods.

Experimental Research on Evaluation of Soil Water Content Using Ground Penetrating Radar and Wavelet Packet-Based Energy Analysis

Soil water content is one of the most important factors affecting the safety and stability of buildings or structures, especially in roadbeds, slopes, earth dams and foundations. Accurate assessments of soil water content can ensure the quality of construction, reduce construction costs and prevent accidents, among other benefits. In this study, ground penetrating radar (GPR) was used to detect and evaluate changes in soil water content. The GPR signal is usually nonstationary and nonlinear; however, traditional Fourier theory is typically suitable for periodic stationary signals, and cannot reflect the law of the frequency and energy of the GPR signal changing with time. Wavelet transform has good time-frequency localization characteristics, and therefore represents a new method for analyzing and processing GPR signals. According to the time-frequency characteristics of GPR signals, in this paper, a new biorthogonal wavelet basis which was highly matched with the GPR waveform was constructed using the lifting framework of wavelet theory. Subsequently, an evaluation method, namely, the wavelet packet-based energy analysis (WPEA) method, was proposed. The method was utilized to calculate the wavelet packet-based energy indexes (WPEI) of the GPR single-channel signals for clay samples with water contents ranging from 10% to 24%. The research results showed that there was a highly correlated linear relationship between the WPEI and the soil water contents, and the relationship between the two was fitted with a linear fitting function. The feasibility of the method was verified by comparing our results with those obtained using classical wavelet bases to perform the wavelet packet transform. The large-area, continuous scanning measurement method of GPR was shown to be suitable for evaluations of soil water contents in roadbeds, slopes, earth dams, and foundations.

Sparse inversion-based seismic random noise attenuation via self-paced learning

Seismic random noise reduction is an important task in seismic data processing at the Chinese loess plateau area, which benefits the geologic structure interpretation and further reservoir prediction. The sparse inversion is one of the widely used tools for seismic random noise reduction, which is often solved via the sparse approximation with a regularization term. The ℓ1 norm and total variation (TV) regularization term are two commonly used regularization terms. However, the ℓ1 norm is only a relaxation of the ℓ0 norm, which cannot always provide a sparse result. The TV regularization term may provide unexpected staircase artifacts. To avoid these disadvantages, we proposed a workflow for seismic random noise reduction by using the self-paced learning (SPL) scheme and a sparse representation (i.e. the continuous wavelet transform, CWT) with a mixed norm regularization, which includes the ℓp norm and the TV regularization. In the implementation, the SPL, which is inspired by human cognitive learning, is introduced to avoid the bad minima of the non-convex cost function. The SPL can first select the high signal-to-noise ratio (SNR) seismic data and then gradually select the low SNR seismic data into the proposed workflow. Moreover, the generalized Beta wavelet (GBW) is adopted as the basic wavelet of the CWT to better match for seismic wavelets and then obtain a more localized time-frequency (TF) representation. It should be noted that the GBW can easily constitute a tight frame, which saves the calculation time. Synthetic and field data examples are adopted to demonstrate the effectiveness of the proposed workflow for effectively suppressing seismic random noises and accurately preserving valid seismic reflections.

The Altes Family of Log-Periodic Chirplets and the Hyperbolic Chirplet Transform

This work revisits a class of biomimetically inspired waveforms introduced by R.A. Altes in the 1970s for use in sonar detection. Similar to the chirps used for echolocation by bats and dolphins, these waveforms are log-periodic oscillations, windowed by a smooth decaying envelope. Log-periodicity is associated with the deep symmetry of discrete scale invariance in physical systems. Furthermore, there is a close connection between such chirping techniques, and other useful applications such as wavelet decomposition for multi-resolution analysis. Motivated to uncover additional properties, we propose an alternative, simpler parameterisation of the original Altes waveforms. From this, it becomes apparent that we have a flexible family of hyperbolic chirps suitable for the detection of accelerating time-series oscillations. The proposed formalism reveals the original chirps to be a set of admissible wavelets with desirable properties of regularity, infinite vanishing moments and time-frequency localisation. As they are self-similar, these “Altes chirplets” allow efficient implementation of the scale-invariant hyperbolic chirplet transform (HCT), whose basis functions form hyperbolic curves in the time-frequency plane. Compared with the rectangular time-frequency tilings of both the conventional wavelet transform and the short-time Fourier transform, the HCT can better facilitate the detection of chirping signals, which are often the signature of critical failure in complex systems. A synthetic example is presented to illustrate this useful application of the HCT.

A multi scale time–frequency analysis on Electroencephalogram signals

It is well known, the Electroencephalogram (EEG) signals are non-stationary signals which helps us in understanding the complex brain dynamics, cognitive processes, etc. In this paper, we have analysed the healthy and Epilepsy seizure subjects through continuous wavelet transform using Morlet wavelet function. We identify the key differences between healthy and epilepsy seizure EEG signals’ low frequency periodic modulations and transient time varying patterns. Persistent intermixing of alpha and beta waves is found to be a key characteristic feature of the patients. The frequency intermixing is completely absent in signals from the hippocampal formation of the opposite hemisphere of the brain for the patients without seizure, akin to the healthy subjects. Our study further reveals dominance of frequency broadened gamma waves for seizure patients as compared to the low frequency regular alpha and beta waves for the healthy subjects. The time–frequency localization of wavelet transform clearly shows transfer of power to high frequency beta waves from the low frequency alpha waves in the signals of the epileptogenic zone of the patients. The observed frequency intermixing, reported here, is analogous to the bi-stability behaviour of dynamical systems.

Underwater Target Localization Using Opportunistic Ship Noise Recorded on a Compact Hydrophone Array

In this research, a new application using broadband ship noise as a source-of-opportunity to estimate the scattering field from the underwater targets is reported. For this purpose, a field trial was conducted in collaboration with JASCO Applied Sciences at Duncan’s Cove, Canada in September 2020. A hydrophone array was deployed in the outbound shipping lane at a depth of approximately 71 m to collect broadband noise data from different ship types and effectively localize the underwater targets. In this experiment, a target was installed at a distance (93 m) from the hydrophone array at a depth of 25 m. In this study, a matched field processing (MFP) algorithm is utilized for localization. Different propagation models are presented using Green’s function to generate the replica signal; this includes normal modes in a shallow water waveguide, the Lloyd-mirror pattern for deep water, as well as the image model. We use the MFP algorithm with different types of underwater environment models and a proposed estimator to find the best match between the received signal and the replica signal. Finally, by applying the scatter function on the proposed multi-channel cross correlation coefficient time-frequency localization algorithm, the location of target is detected.

Signal Recognition for English Speech Translation Based on Improved Wavelet Denoising Method

The signal corresponding to English speech contains a lot of redundant information and environmental interference information, which will produce a lot of distortion in the process of English speech translation signal recognition. Based on this, a large number of studies focus on encoding and processing English speech, so as to achieve high-precision speech recognition. The traditional wavelet denoising algorithm plays an obvious role in the recognition of English speech translation signals, which mainly depends on the excellent local time-frequency domain characteristics of the wavelet signal algorithm, but the traditional wavelet signal algorithm is still difficult to select the recognition threshold, and the recognition accuracy is easy to be affected. Based on this, this paper will improve the traditional wavelet denoising algorithm, abandon the single-threshold judgment of the original traditional algorithm, innovatively adopt the combination of soft threshold and hard threshold, further solve the distortion problem of the denoising algorithm in the process of English speech translation signal recognition, improve the signal-to-noise ratio of English speech recognition, and further reduce the root mean square error of the signal. Good noise reduction effect is realized, and the accuracy of speech recognition is improved. In the experiment, the algorithm is compared with the traditional algorithm based on MATLAB simulation software. The simulation results are consistent with the actual theoretical results. At the same time, the algorithm proposed in this paper has obvious advantages in the recognition accuracy of English speech translation signals, which reflects the superiority and practical value of the algorithm.

A novel method based on matching pursuit decomposition of gait signals for Parkinson’s disease, Amyotrophic lateral sclerosis and Huntington’s disease detection

Background and ObjectiveAn accurate detection of neurodegenerative diseases (NDDs) definitely improves the life of patients and has attracted growing attention. MethodsIn this paper, a general automatic method for detection of Parkinson’s disease (PD), Amyotrophic lateral sclerosis (ALS) and Huntington’s disease (HD) has been proposed based on the localized time–frequency information of gait signals. The new main part of the detection method is to obtain a small set of sparse coefficients for the local representation of gait signals with appropriate time and frequency resolution. For this purpose, a hybrid feature set based on sparse matching pursuit decomposition and two sets of nonlinear and linear features has been developed. Then, principal components of the proposed feature have been analyzed using a sparse coding classifier.ResultsThe proposed approach has achieved high average accuracy rates of 93%, 94%, and 97% for PD, ALS, and HD detection, respectively. ConclusionsThe obtained results have indicated that combination of time and frequency information of the gait signals through adaptive localized window length in MP makes it more efficient in comparison with the existing time, frequency or other time–frequency gait parameters. The great potential of nonlinear sparse features for PD and HD detection and linear ones for ALS detection has also been shown.

A Statistical Method for Exploratory Data Analysis Based on 2D and 3D Area under Curve Diagrams: Parkinson's Disease Investigation.

A statistical method for exploratory data analysis based on 2D and 3D area under curve (AUC) diagrams was developed. The method was designed to analyze electroencephalogram (EEG), electromyogram (EMG), and tremorogram data collected from patients with Parkinson’s disease. The idea of the method of wave train electrical activity analysis is that we consider the biomedical signal as a combination of the wave trains. The wave train is the increase in the power spectral density of the signal localized in time, frequency, and space. We detect the wave trains as the local maxima in the wavelet spectrograms. We do not consider wave trains as a special kind of signal. The wave train analysis method is different from standard signal analysis methods such as Fourier analysis and wavelet analysis in the following way. Existing methods for analyzing EEG, EMG, and tremor signals, such as wavelet analysis, focus on local time–frequency changes in the signal and therefore do not reveal the generalized properties of the signal. Other methods such as standard Fourier analysis ignore the local time–frequency changes in the characteristics of the signal and, consequently, lose a large amount of information that existed in the signal. The method of wave train electrical activity analysis resolves the contradiction between these two approaches because it addresses the generalized characteristics of the biomedical signal based on local time–frequency changes in the signal. We investigate the following wave train parameters: wave train central frequency, wave train maximal power spectral density, wave train duration in periods, and wave train bandwidth. We have developed special graphical diagrams, named AUC diagrams, to determine what wave trains are characteristic of neurodegenerative diseases. In this paper, we consider the following types of AUC diagrams: 2D and 3D diagrams. The technique of working with AUC diagrams is illustrated by examples of analysis of EMG in patients with Parkinson’s disease and healthy volunteers. It is demonstrated that new regularities useful for the high-accuracy diagnosis of Parkinson’s disease can be revealed using the method of analyzing the wave train electrical activity and AUC diagrams.

Epileptic EEG Classification by Using Time-Frequency Images for Deep Learning.

Epilepsy is one of the most common brain disorders worldwide. The most frequently used clinical tool to detect epileptic events and monitor epilepsy patients is the EEG recordings. There have been proposed many computer-aided diagnosis systems using EEG signals for the detection and prediction of seizures. In this study, a novel method based on Fourier-based Synchrosqueezing Transform (SST), which is a high-resolution time-frequency (TF) representation, and Convolutional Neural Network (CNN) is proposed to detect and predict seizure segments. SST is based on the reassignment of signal components in the TF plane which provides highly localized TF energy distributions. Epileptic seizures cause sudden energy discharges which are well represented in the TF plane by using the SST method. The proposed SST-based CNN method is evaluated using the IKCU dataset we collected, and the publicly available CHB-MIT dataset. Experimental results demonstrate that the proposed approach yields high average segment-based seizure detection precision and accuracy rates for both datasets (IKCU: 98.99% PRE and 99.06% ACC; CHB-MIT: 99.81% PRE and 99.63% ACC). Additionally, SST-based CNN approach provides significantly higher segment-based seizure prediction performance with 98.54% PRE and 97.92% ACC than similar approaches presented in the literature using the CHB-MIT dataset.