Time-frequency Matrix Research Articles

A Kaiser Window-Based S-Transform for Time-Frequency Analysis of Power Quality Signals

The accurate time-frequency (TF) positioning of power quality (PQ) disturbances is the basis of dealing with PQ problems in power systems. To accurately detect PQ disturbances, this article proposes a Kaiser window-based S-transform (KST) that provides better time resolution at fundamental frequency to detect the amplitude information for voltage swell, sag, interrupt, flicker, and better frequency resolution at higher frequencies to detect the frequency of time-varying harmonics and oscillatory transient. Based on short-time Fourier transform and S-transform, KST uses a Kaiser window with the characteristic of inherent optimal energy concentration as the kernel function. The Kaiser window can be adjusted adaptively according to the detection demand of PQ disturbances by the designed control function. This allows KST to easily accommodate different detection requirements at different frequencies. The utilization of Fourier transform ensures that KST can be realized quickly. The complex TF matrix is generated after a signal is transformed by KST, where the column vector is expressed as the distribution of amplitude and phase with time at a certain frequency, and the row vector represents the distribution of amplitude and phase with frequency at a certain sampling time. Experimental results demonstrate that the proposed KST significantly outperforms the state-of-the-art techniques in TF analysis of PQ signals, especially for the energy concentration and the detection of fundamental wave.

Synchroextracting chirplet transform-based epileptic seizures detection using EEG

With the development of computer technology, computer-aided medical diagnosis based on signal processing is trending up. In recent years, the detection of epilepsy electroencephalogram (EEG) signals for clinical application has attracted extensive attention from many researchers. In this paper, a novel epilepsy classification model is proposed based on the time-frequency (TF) analysis method named synchroextracting chirplet transform (SECT). The energy concentrated TF representation of the signal is first obtained benefit by the introduced parameter chirp rate. Then the instantaneous frequency (IF) trajectory is estimated by extracting the TF coefficients most relevant to the signal through the synchroextracting chirplet operator (SECO). The original signal can be simple and effectively reconstructed using the accurate IF trajectory with anti-noise interference ability. Singular value decomposition is performed on the TF matrix to obtain the feature vectors with strong characterization capacity for different epilepsy behaviors, and the multiple classification tasks are finally completed with support vector machine (SVM) classifier. Two authoritative epilepsy datasets are employed in our work to verify the effectiveness of the proposed scheme. No less than 99.17 % accuracy, 99.33 % specificity, and 99.28 % sensitivity are achieved on a total of ten classification tasks that are closely related to the actual clinical applications in the Bonn dataset; an average of 99.29 % accuracy and 0.97 matthews correlation coefficient (MCC) are obtained among all subjects in the long-term EEG database CHB-MIT. The noise robustness and portability of our proposal are verified through the stable experimental results. The superior detection accuracy also provides clinicians with auxiliary diagnosis.

Underwater reverberation suppression based on non-negative matrix factorisation

Reverberation is the main background interference in underwater active sonar target detection that seriously interferes with the extraction of the target highlight echo. In consideration of the difference in the time-frequency distributions of the target highlight echo and reverberation, an underwater reverberation suppression method based on non-negative matrix factorisation is proposed in this study. The Wigner-Ville time-frequency matrix of the underwater target echo is used as the input, and non-negative matrix factorisation is applied to express the time-frequency matrix as a low-rank matrix. The influences of rank selection on the reverberation suppression effect and signal expression of the target highlight echo are analysed. Given that the time-frequency matrix of the target highlight echo cannot be expressed in the low-rank form when transmitting linear frequency modulation signal, this matrix is processed with low-rank preprocessing through matrix rotation. The components of the target highlight echo, which can be expressed in the form of a low-rank matrix, are preserved. By contrast, the components of the reverberation interference, which cannot be represented in such a form, are removed in the underwater target echoes. The simulation and experimental results show that the algorithm can effectively improve the signal-to-reverberation ratio of underwater target echoes.

Hyperbolic Window S-Transform Aided Deep Neural Network Model-Based Power Quality Monitoring Framework in Electrical Power System

With the fast development of power grid the usage of electrical equipments is increased which led to importance of power quality disturbance sensing for reliable and smooth operation. In this paper, a deep neural network has been designed using stacked autoencoder (SAE) for deep feature extraction from time-frequency spectrum of single and combined PQ disturbances in electrical power system network. For this purpose, synthetic PQ signals are analyzed in time-frequency domain through hyperbolic window stockwell transform (HWST). Thereafter, PQ signal converted HWST time-frequency matrix has been grouped into time-frequency blocks and subsequently fed as input to 3-layer stacked autoencoder model (SAE) for deep feature learning. Finally, the extracted deep features are classified through several machine learning classifier. The results indicate that proposed framework using XGboost classifier can classify 18 different single and combined PQ event with a 99.86% accuracy. The proposed framework also yields satisfactory outcome with real life PQ data. Therefore, proposed framework can be implemented for Power quality monitoring in electrical power system.

Signal time–frequency representation and decomposition using partial fractions

Summary The Z-transform of a complex time signal (or the analytic signal of a real signal) is equal to the Z-transform of a prediction error divided by the Z-transform of the prediction error operator. This inverse is decomposed into a sum of partial fractions, which are used to obtain impulse response operators formed by non-causal filters that complex-conjugate symmetric coefficients. The time components are obtained by convolving the filters with the original signal, and the peak frequencies, corresponding to the poles of the prediction error operator, are used for mapping the time components into frequency components. For non-stationary signals, this decomposition is done in sliding time windows, and the signal component values, in the middle of each window, are attributed to the peak value of its frequency response that corresponds to the pole of this partial fraction component. The result is an exact, but non-unique, time–frequency representation of the input signal. A sparse signal decomposition can be obtained by summing along the frequency axis in patches with similar characteristics in the time–frequency domain. The peak amplitude frequency of each new time component is obtained by computing a scalar prediction error operator in sliding time windows, resulting in a sparse time–frequency representation. In both cases, the result is a time–frequency matrix where an estimate of the frequency content of the input signal can be obtained by summation over the time variable. The performance of the new method is demonstrated with excellent results on a synthetic time signal, the LIGO gravitational wave signal and seismic field data.

Envelope Tracking Power Amplifier Using Short-Time Fourier Transform

A new power amplifier (PA) efficiency enhancement technique using short-time Fourier transform (STFT) in envelope tracking (ET) topology is introduced. The proposed technique produced a time-frequency matrix that illustrated the signal spectrum at each time frame. The applied filter was made time variant by setting a threshold for the preserved power percentage at each time frame. The technique gave full control over the tradeoff between bandwidth (BW) reduction and power consumption efficiency and provided a significant BW reduction over pure ET. The proposed method was demonstrated on a 37 dBm, 40-MHz long-term evolution signal at 2.4 GHz, using 65 W 3-dB compression-point GaN PA. The resulting efficiencies were 38.6% [16-quadrature amplitude modulation (QAM)] and 41.9% (64-QAM).

Non-negative matrix factorization-based time-frequency feature extraction of voice signal for Parkinson's disease prediction

Parkinson's disease (PD) is a neuron related disorder that affects the people in old age. The majority of people suffering from PD develop several voice impairments mainly related to what is known as dysarthric speech. Voice analysis can help in PD detection and in the evaluation of the dysarthria level of the patients. This study introduces time-frequency features to model discontinuities and abrupt changes that arise in the voice signal due to PD. The proposed method consists of four stages: time-frequency matrix (TFM) representation, TFM decomposition using non-negative matrix factorization (NMF), feature extraction and classification. Statistical analyses show that the proposed time-frequency features significantly differentiate between PD patients and healthy speakers. Experiments with sustained vowel phonations and isolated words of the corpus PC–GITA are conducted. The proposed method achieved average classification accuracies of up to 92% in vowels, and 97% in words. There is an improvement in accuracy ranging from 10% to 40% compared to existing methods. Further, the developed models are evaluated upon an independent dataset. Results on this separate test set show accuracies ranging from 63% to 75% in vowels, and from 53% to 75% in isolated words. Regarding the dysarthria level evaluation, Spearman's correlations between original and predicted labels are around 0.81 in sustained vowels and in isolated words. The results indicate that the proposed approach is suitable and robust for the automatic detection of PD.

ROC Analysis of EEG Subbands for Epileptic Seizure Detection using Naïve Bayes Classifier

This paper presents analysis of Electroencephalograms (EEGs) and subbands (delta, theta, alpha, beta, gamma) using image descriptors for epileptic seizure detection. Short-time Fourier transform (STFT) has been utilized to convert 1-D EEG data into image. All subbands are separated from the time-frequency (t-f) matrix and Haralick features of each subband is fed in the Naïve Bayes (NB) classifier. Receiver operating characteristic (ROC) analysis has been used for performance evaluation of classifier. Among all subbands, gamma band alone shows a maximum AUC of 0.98 to classify between ictal and healthy class, while beta band shows a maximum AUC of 0.96 to differentiate between ictal and interictal class. Significance of this work is it shows the medical advantage of different subbands for the detection process.

Application of a noise reduction method combining AVMD and SVD in natural gas pipeline leakage signal

Due to the large amount of noise in pipeline leakage signal, the accuracy of the leakage detection device's judgment will be reduced by direct leakage detection. Therefore, the noise reduction of pipeline leakage signal is critical for preprocessing technology of pipeline leakage detection. A denoising method combining adaptive variational mode decomposition (AVMD) and singular value decomposition (SVD) is proposed in this paper. First, the mode number and the penalty factor of VMD are searched automatically by AVMD. The AVMD algorithm is coupled to a fitness function based on improved refine composite multiscale dispersion entropy (RCMDE). Subsequently, a time–frequency matrix which obtains time–frequency subspace after SVD is constructed for all mode components decomposed by VMD, and the number of effective time–frequency subspaces is determined by the relative change rate of singular values, thereby the denoised signal is achieved. Finally, the experimental results show that the AVMD-SVD method proposed in this paper has the significant denoising effect and strong robustness.

An Improved Multi-Ridge Extraction Method Based on Differential Synchro-Squeezing Wavelet Transform

It is very important to accurately extract the instantaneous frequency (IF) of complex non-stationary signals, so the signal processing methods based on IF are widely used in engineering. However, in non-stationary complex vibration signals, it is difficult to extract the instantaneous frequency under strong noise because the frequency changes rapidly. This paper proposes an improved multi-ridge extraction method based on differential synchro-squeezing wavelet transform (DSWT). First, an improved method DSWT is proposed to reduce the computation time and image noise of synchro-squeezing wavelet transform (SWT). The running time of the algorithm can be further reduced by segmenting the signal and compressing the time-frequency matrix. The image noise can be significantly reduced by differentiating SWT time-frequency matrix. It lays a good foundation for the extraction of the time-frequency ridge line. Secondly, an improved multi-ridge extraction method is proposed. The ridge jump due to end effect can be eliminated adaptively in segmented extraction. It further improves the time-frequency aggregation and extraction effect of the wavelet ridgeline image. Finally, the improved multi-ridge extraction method based on DSWT (DSWT-IMRE) is verified by the simulation data and experimental data under different conditions. Compared with the method proposed in previous study, the results show that DSWT-IMRE has higher extraction accuracy.

An Imbalanced Fault Diagnosis Method for Rolling Bearing Based on Semi-Supervised Conditional Generative Adversarial Network With Spectral Normalization

In actual industrial applications, rolling bearings are under normal working conditions most of the time, and the fault data that can be collected are insufficient, so they are prone to data imbalance. Due to the high cost of labeling all fault data, most fault data are unlabeled. In this study, the Semi-supervised Conditional Generative Adversarial Network with Spectral Normalization (SN-SSCGAN) is proposed to solve these problems. Its core idea is to generate new samples with similar distribution by using partially labeled minority fault samples to balance the dataset. First, this method first applies wavelet transform to preprocess a vibration signal and obtain a time-frequency matrix. Second, the partially labeled time-frequency fault data are taken as the input of SN-SSCGAN, Nash equilibrium is achieved through adversarial training, and then data with similar distribution are generated. Lastly, the generated fault data are added to the dataset for balancing, and a convolutional neural network is used for fault diagnosis. The effectiveness of the proposed method is verified with comparative experiments in the CWRU bearing dataset. Results show that this method can generate high-quality samples and determine satisfactory results in bearing fault diagnosis when only a small number of labeled samples and the remaining unlabeled samples are used.

Gesture Recognition Based on Multiscale Singular Value Entropy and Deep Belief Network

As an important research direction of human–computer interaction technology, gesture recognition is the key to realizing sign language translation. To improve the accuracy of gesture recognition, a new gesture recognition method based on four channel surface electromyography (sEMG) signals is proposed. First, the S-transform is applied to four channel sEMG signals to enhance the time-frequency detail characteristics of the signals. Then, multiscale singular value decomposition is applied to the multiple time-frequency matrix output of S-transform to obtain the time-frequency joint features with better robustness. The corresponding singular value permutation entropy is calculated as the eigenvalue to effectively reduce the dimension of multiple eigenvectors. The gesture features are used as input into the deep belief network for classification, and nine kinds of gestures are recognized with an average accuracy of 93.33%. Experimental results show that the multiscale singular value permutation entropy feature is especially suitable for the pattern classification of the deep belief network.

A new acoustic emission damage localization method using synchrosqueezed wavelet transforms picker and time-order method

Acoustic emission technique, as a passive structural health monitoring technique, has been widely applied to detecting and locating the structural damage. The time difference of arrival and the wave velocity are the key factors in most of the acoustic emission localization methods, and the accuracy of these two factors will affect the accuracy of damage localization. To improve the accuracy of damage localization, this article proposes a new damage localization method based on the synchrosqueezed wavelet transform picker and the time-order method. The synchrosqueezed wavelet transform picker, which picks the time–frequency similar point based on time–frequency similarity theory in the low-noise interval of time–frequency matrix, can improve the accuracy and robustness of calculating time difference of arrival. Meanwhile, the time-order method not only measures the wave velocity in real time but also reduces the computing time by appropriately arranging the distribution of acoustic emission sensors. These advantages improve the accuracy and robustness of acoustic emission localization, which was verified by experiments. Furthermore, the new localization method was employed to study the energy distribution in the embedded section of steel bar during the pull-out test of steel bar and concrete, and the results show the types of resistance between steel bar and concrete.

Fractional frequency band entropy for bearing fault diagnosis under varying speed conditions

Fault diagnosis under varying speed conditions has become a research hotspot in rotating machinery monitoring. Due to the energy concentration property of linear frequency-modulated signals, fractional Fourier transform (FrFT) is helpful to bearing fault detection with varying speed. However, its performance depends on FrFT filter parameters, which are difficult to determine. So fractional frequency band entropy (FrFBE) is proposed to solve this problem, constructing optimized FrFT filter to extract time-varying fault characteristics. First, short-time fractional Fourier transform (STFrFT) is performed on the demodulated signal. Then, FrFBE is developed based on the obtained fractional time-frequency matrix to locate aggregation positions of fault harmonics. Next, a global/local minimum FrFBE criterion is proposed to determine FrFT filtering centers. Finally, the fault characteristics are extracted by computed order tracking (COT) from the filtered results. Simulation and experiment cases show good diagnosis result with different operating conditions, with recognition error kept within 1%.

Distinguishing polymeric insulators PD sources through RF PD measurement

A better performance and consequently the widespread use of polymeric insulators in different parts of the power grid can increase their role in the grid reliability. The accumulation of contamination and housing-erosion are the two most effective factors in undermining the performance of this type of insulators. Therefore, electric utilities need to identify contaminated insulators for washing and cracks in polymeric housing to replace them with healthy specimens. This paper discusses the impact of contamination layer and housing-erosion of polymeric insulators on the partial discharges (PD) at the insulator surface, through RF-PRPD (phase resolved partial discharge) patterns. The existence of different sources of PDs in a real environment (transmission line or station) makes it difficult to use the PRPD patterns to distinguish them from each other. Therefore, using a conical monopole antenna, the simultaneous PD signals and the related RF-PRPD pattern of samples under test are captured. The grayscale image was obtained using the time-frequency matrix of the PD signals transform, by wavelet. Then, features are extracted and selected from grayscale image. By clustering of the PD signals, the resulted RF-PRPD sub-patterns are well separated and provided the necessary means to distinguish among the status of different samples under test.

A combined kernel-based fuzzy C-means clustering and spectral centroid for instantaneous frequency estimation

An improved instantaneous frequency estimation algorithm for rotating machines based on a kernel-based fuzzy C-means clustering (KFCM) algorithm used in association with a spectral centroid algorithm is proposed in this study. The clustering algorithm is used first to discriminate the time-frequency points from the sources of the reference axis and other points. The discrete time-frequency points related to the instantaneous rotation frequency of the reference axis are then located based on the values of the time-frequency matrix elements; on the basis of these elements, the instantaneous rotation frequency is then estimated using a spectral centroid algorithm. It is demonstrated that this method effectively reduces the effects of interference and noise while achieving higher estimation precision. To validate the proposed method, numerical simulations of multi-component signals and crossover signals are performed. The results of these simulations indicate that the method can realize instantaneous frequency estimation with high precision, even when the numerical responses are contaminated by Gaussian white noise. In addition, when this method is used to analyze the vibration signal of rotating machinery in the situation of a run-up procedure, remarkable speed estimation results are obtained.

Study on fiber fracture sequence during yarn tensile fracture via acoustic emission method

via the acoustic emission technology, a method used for investigating the single fiber fracture sequence during tensile fracture process of blended yarn, which is made of different kinds of fiber was presented in this paper. As the fibers aggregate together after spinning process, the tensile strength of the yarn mainly originates from the strength of the fibers inside the yarn, as well as the cohesive force and surface friction between the fibers. In order to collect the acoustic emission signals generated during tensile fracture of the yarn and different single fibers, the acoustic emission technology was adopted. Firstly, the time-frequency matrix of the acoustic emission signal was constructed on the basis of Hilbert-Huang transform; subsequently, the singular value of the signal was obtained by singular value decomposition of the time-frequency matrix of the signal; ultimately, the singular value of the signal was judged by the fuzzy c-means cluster analysis. The results showed that the singular value can be used not only to characterize the fractures of different kinds of fiber in an efficient way, but also to identify the fiber fracture sequence during tensile fracture process of blended yarn, providing an excellent theoretical support for researching into the yarn formation process.

Automated sleep apnea detection from cardio-pulmonary signal using bivariate fast and adaptive EMD coupled with cross time–frequency analysis

Sleep apnea is a sleep related pathology in which breathing or respiratory activity of an individual is obstructed, resulting in variations in the cardio-pulmonary (CP) activity. The monitoring of both cardiac (heart rate (HR)) and pulmonary (respiration rate (RR)) activities are important for the automated detection of this ailment. In this paper, we propose a novel automated approach for sleep apnea detection using the bivariate CP signal. The bivariate CP signal is formulated using both HR and RR signals extracted from the electrocardiogram (ECG) signal. The approach consists of three stages. First, the bivariate CP signal is decomposed into intrinsic mode functions (IMFs) and residuals for both HR and RR channels using bivariate fast and adaptive empirical mode decomposition (FAEMD). Second, the features are extracted using time-domain analysis, spectral analysis, and time–frequency domain analysis of IMFs from CP signal. The time–frequency domain features are computed from the cross time–frequency matrices of IMFs of CP signal. The cross time–frequency matrix of each IMF is evaluated using the Stockwell (S)-transform. Third, the support vector machine (SVM) and the random forest (RF) classifiers are used for automated detection of sleep apnea with the features from the bivariate CP signal. Our proposed approach has demonstrated an average sensitivity and specificity of 82.27% and 78.67%, respectively for sleep apnea detection using the 10-fold cross-validation method. The approach has yielded an average sensitivity and specificity of 73.19% and 73.13%, respectively for the subject-specific cross-validation. The performance of the approach was compared with other CPC features used for the detection of sleep apnea.

Time-Frequency Domain Deep Convolutional Neural Network for the Classification of Focal and Non-Focal EEG Signals

The neurological disease such as the epilepsy is diagnosed using the analysis of electroencephalogram (EEG) recordings. The areas of the brain associated with the consequence of epilepsy are termed as epileptogenic regions. The focal EEG signals are generated from epileptogenic areas, and the nonfocal signals are obtained from other regions of the brain. Thus, the classification of the focal and non-focal EEG signals are necessary for locating the epileptogenic areas during surgery for epilepsy. In this paper, we propose a novel method for the automated classification of focal and non-focal EEG signals. The method is based on the use of the synchrosqueezing transform (SST) and deep convolutional neural network (CNN) for the classification. The time-frequency matrices of EEG signal are evaluated using both Fourier SST (FSST) and wavelet SST (WSST). The two-dimensional (2D) deep CNN is used for the classification using the time-frequency matrix of EEG signals. The experimental results reveal that the proposed method attains the accuracy, sensitivity, and specificity values of more than 99% for the classification of focal and non-focal EEG signals. The method is compared with existing approaches for the discrimination of focal and non-focal categories of EEG signals.

Automated detection of heart valve diseases using chirplet transform and multiclass composite classifier with PCG signals

Heart valve diseases (HVDs) are a group of cardiovascular abnormalities, and the causes of HVDs are blood clots, congestive heart failure, stroke, and sudden cardiac death, if not treated timely. Hence, the detection of HVDs at the initial stage is very important in cardiovascular engineering to reduce the mortality rate. In this article, we propose a new approach for the detection of HVDs using phonocardiogram (PCG) signals. The approach uses the Chirplet transform (CT) for the time–frequency (TF) based analysis of the PCG signal. The local energy (LEN) and local entropy (LENT) features are evaluated from the TF matrix of the PCG signal. The multiclass composite classifier formulated based on the sparse representation of the test PCG instance for each class and the distances from the nearest neighbor PCG instances are used for the classification of HVDs such as mitral regurgitation (MR), mitral stenosis (MS), aortic stenosis (AS), and healthy classes (HC). The experimental results show that the proposed approach has sensitivity values of 99.44%, 98.66%, and 96.22% respectively for AS, MS and MR classes. The classification results of the proposed CT based features are compared with existing approaches for the automated classification of HVDs. The proposed approach has obtained the highest overall accuracy as compared to existing methods using the same database. The approach can be considered for the automated detection of HVDs with the Internet of Medical Things (IOMT) applications.