Quadratic Time-frequency Distributions Research Articles

An improved signal-dependent QTFD based on iterative regional RGK optimization for multi-component LFM signals

It is quite challenging for the quadratic time-frequency distribution (QTFD) to analyze the multi-component linear frequency modulation (MC-LFM) signals due to its inevitable cross-term issue, particularly in the case of simultaneous strong components and weak components involved in the MC-LFM signals. This paper proposes a novel signal-dependent QTFD based on regional radially Gaussian kernel (RRGK) to improve the time-frequency representations (TFR) of the MC-LFM signals with distinguishing component amplitudes. The model of MC-LFM signals is firstly introduced, and the detrended Radon transform of ambiguity domain (RTA) technique is combined with energy distribution feature in the ambiguity domain analysis for the detection of potential auto-terms concentrated along lines passing through the origin of the Doppler-lag plane. The combined two-step signal detection method can be easily extended to other signal-dependent QTFDs. Then the Doppler-lag distribution area of each detected auto-term is automatically selected with stronger components peeled to restrict the searching area of RGK. Afterwards, a novel iterative regional RGK-based TFD (IRRGD) is developed to resolve strong and weak components under a proper trade-off between auto-term resolution and cross-term suppression in the TFD. Finally, filtering is performed in (t, f) domain to further improve the TFD results. Also, a quantitative indicator is proposed to measure weak signal preservation. Both simulation and experimental results have verified the superiorities of the proposed method over other existing state-of-the-art algorithms.

Induction Machine Fault Diagnosis With Quadratic Time–Frequency Distributions: State of the Art

Induction Machine Fault Diagnosis With Quadratic Time–Frequency Distributions: State of the Art

EEG-Based Mental Tasks Recognition via a Deep Learning-Driven Anomaly Detector.

This paper introduces an unsupervised deep learning-driven scheme for mental tasks' recognition using EEG signals. To this end, the Multichannel Wiener filter was first applied to EEG signals as an artifact removal algorithm to achieve robust recognition. Then, a quadratic time-frequency distribution (QTFD) was applied to extract effective time-frequency signal representation of the EEG signals and catch the EEG signals' spectral variations over time to improve the recognition of mental tasks. The QTFD time-frequency features are employed as input for the proposed deep belief network (DBN)-driven Isolation Forest (iF) scheme to classify the EEG signals. Indeed, a single DBN-based iF detector is constructed based on each class's training data, with the class's samples as inliers and all other samples as anomalies (i.e., one-vs.-rest). The DBN is considered to learn pertinent information without assumptions on the data distribution, and the iF scheme is used for data discrimination. This approach is assessed using experimental data comprising five mental tasks from a publicly available database from the Graz University of Technology. Compared to the DBN-based Elliptical Envelope, Local Outlier Factor, and state-of-the-art EEG-based classification methods, the proposed DBN-based iF detector offers superior discrimination performance of mental tasks.

Time-frequency readability enhancement of compact support kernel-based distributions using image post-processing: Application to instantaneous frequency estimation of M-ary frequency shift keying signals

Time-frequency distributions (TFDs) based on time-lag kernels with compact support (KCS) have proved their high performance in terms of resolution and crossterms suppression. However, as for all kernel-based quadratic TFDs, these distributions suffer from spreading out signal terms. This is due to the unavoidable smoothing effects of the kernel in the ambiguity domain. The main objective of this paper is to improve concentration, interference rejection and so time-frequency localization of this representation class. The latter has the advantage of being tuned using a single parameter while external windows are no longer needed. The KCS-TFDs, referred to as KCSDs, are first optimized using a selection of the most used objective performance measures in the literature. Important signal features are extracted as well through analysis of time slice plots. The obtained TF diagrams are then enhanced using a specific method that includes two-dimensional Wiener filter, automatic binarization and morphological image processing techniques. The enhanced plots are compared to those obtained from the original TFDs using several tests on real-life and multicomponent frequency modulated (FM) signals including the noise effects. Moreover, a comparative study involving a selection of the best-performing reassignment time-frequency distributions is provided. The obtained results show a significant improvement of concentration, time-frequency localization of the autoterms as well as interference and noise suppression. As viable applications, the proposed approach is used first to instantaneous frequency (IF) estimation of several synthetic and real-life M-ary frequency shift keying (MFSK) signals. It is shown that the IF estimator from the enhanced plots performs better than smoothed pseudo Wigner-Ville distribution (SPWVD) and reassignment post-processing-based TFDs in terms of mainlobe width (MLW) and variance, respectively, even at low signal-to-noise ratio (SNR). On the other hand, time-frequency characterization of continuous wave linear frequency modulation (CW-LFM) and pulse linear FM (PLFM) radar signals is also investigated.

An improved signal-dependent quadratic time-frequency distribution using regional compact kernels for analysis of nonstationary multicomponent LFM signals

The time-frequency analysis of nonstationary multicomponent linear frequency modulation (LFM) signals is still a challenging task due to their cross-term interferences. In this paper, a novel signal-dependent adaptive compact kernel based time-frequency distribution (CKD) named regional adaptive CKD (RACKD) is proposed. The proposed RACKD firstly represents the signal in the Doppler-lag (ν, τ) ambiguity domain, and then applies a signal-dependent regional compact kernel to filter the cross-term interferences, with preserving the auto-terms in the ambiguity domain. By automatically selecting the auto-terms' distribution area which represents the signals in the ambiguity domain, the parameters of the newly designed signal-dependent regional compact kernel can be adaptively set according to the signals to be processed. The proposed RACKD shows a more stable performance in the ability of cross-term rejection and component energy of signals concentration around their respective instantaneous frequency, compared to several existing state-of-the-art methods. Both simulation results and experimental results based on sea-truth data have validated the improved performance of the proposed method. For the simulated signal composed of one weak and two strong LFM components with crossing frequency, the proposed RACKD shows up to 2.6% gain as compared to the signal-dependent multidirectional distribution (MDD) approach.

Grading hypoxic-ischemic encephalopathy in neonatal EEG with convolutional neural networks and quadratic time–frequency distributions

Objective. To develop an automated system to classify the severity of hypoxic-ischaemic encephalopathy injury (HIE) in neonates from the background electroencephalogram (EEG). Approach. By combining a quadratic time–frequency distribution (TFD) with a convolutional neural network, we develop a system that classifies 4 EEG grades of HIE. The network learns directly from the two-dimensional TFD through 3 independent layers with convolution in the time, frequency, and time–frequency directions. Computationally efficient algorithms make it feasible to transform each 5 min epoch to the time–frequency domain by controlling for oversampling to reduce both computation and computer memory. The system is developed on EEG recordings from 54 neonates. Then the system is validated on a large unseen dataset of 338 h of EEG recordings from 91 neonates obtained across multiple international centres. Main results. The proposed EEG HIE-grading system achieves a leave-one-subject-out testing accuracy of 88.9% and kappa of 0.84 on the development dataset. Accuracy for the large unseen test dataset is 69.5% (95% confidence interval, CI: 65.3%–73.6%) and kappa of 0.54, which is a significant () improvement over a state-of-the-art feature-based method with an accuracy of 56.8% (95% CI: 51.4%–61.7%) and kappa of 0.39. Performance of the proposed system was unaffected when the number of channels in testing was reduced from 8 to 2—accuracy for the large validation dataset remained at 69.5% (95% CI: 65.5%–74.0%). Significance. The proposed system outperforms the state-of-the-art machine learning algorithms for EEG grade classification on a large multi-centre unseen dataset, indicating the potential to assist clinical decision making for neonates with HIE.

On the Use of High-resolution Time-frequency Distribution Based on a Polynomial Compact Support Kernel for Fault Detection in a Two-level Inverter

Quadratic Time-Frequency Distributions (TFDs) become a standard tool in many fields producing nonstationary signatures. However, these representations suffer from two drawbacks: First, bad time-frequency localization of the signal's autoterms due to the unavoidable crossterms generated by the bilinear form of these distributions. This results on bad estimation of the Instantaneous Frequency (IF) laws and decreases, in our case, the ability to precisely decide the existence of a motor fault. Secondly, the TFD's parameterization is not always straightforward. This paper deals with faults' detection in two-level inverter feeding induction motors, in particular open-circuit Insulated Gate Bipolar Transistor (IGBT) faults. For this purpose, we propose the use of a recent high-resolution TFD, referred as PCBD for Polynomial Cheriet-Belouchrani Distribution. The latter is adjusted using only a single integer that is automatically optimized using the Stankovic concentration measure, otherwise, no external windows are needed to perform the highest time-frequency resolution. The performance of the PCBD is compared to the best-known quadratic representations using a test bench. Experimental results show that the frequency components characterizing open-circuit faults are best detected using the PCBD thanks to its ability to suppress interferences while maintaining the signal's proper terms.

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.

Tonic Cold Pain Detection Using Choi–Williams Time-Frequency Distribution Analysis of EEG Signals: A Feasibility Study

Detecting pain based on analyzing electroencephalography (EEG) signals can enhance the ability of caregivers to characterize and manage clinical pain. However, the subjective nature of pain and the nonstationarity of EEG signals increase the difficulty of pain detection using EEG signals analysis. In this work, we present an EEG-based pain detection approach that analyzes the EEG signals using a quadratic time-frequency distribution, namely the Choi–Williams distribution (CWD). The use of the CWD enables construction of a time-frequency representation (TFR) of the EEG signals to characterize the time-varying spectral components of the EEG signals. The TFR of the EEG signals is analyzed to extract 12 time-frequency features for pain detection. These features are used to train a support vector machine classifier to distinguish between EEG signals that are associated with the no-pain and pain classes. To evaluate the performance of our proposed approach, we have recorded EEG signals for 24 healthy subjects under tonic cold pain stimulus. Moreover, we have developed two performance evaluation procedures—channel- and feature-based evaluation procedures—to study the effect of the utilized EEG channels and time-frequency features on the accuracy of pain detection. The experimental results show that our proposed approach achieved an average classification accuracy of 89.24% in distinguishing between the no-pain and pain classes. In addition, the classification performance achieved using our proposed approach outperforms the classification results reported in several existing EEG-based pain detection approaches.

EEG-based BCI system for decoding finger movements within the same hand

Decoding the movements of different fingers within the same hand can increase the control's dimensions of the electroencephalography (EEG)-based brain–computer interface (BCI) systems. This in turn enables the subjects who are using assistive devices to better perform various dexterous tasks. However, decoding the movements performed by different fingers within the same hand by analyzing the EEG signals is considered a challenging task. In this paper, we present a new EEG-based BCI system for decoding the movements of each finger within the same hand based on analyzing the EEG signals using a quadratic time-frequency distribution (QTFD), namely the Choi–William distribution (CWD). In particular, the CWD is employed to characterize the time-varying spectral components of the EEG signals and extract features that can capture movement-related information encapsulated within the EEG signals. The extracted CWD-based features are used to build a two-layer classification framework that decodes finger movements within the same hand. The performance of the proposed system is evaluated by recording the EEG signals for eighteen healthy subjects while performing twelve finger movements using their right hands. The results demonstrate the efficacy of the proposed system to decode finger movements within the same hand of each subject.

A Deep Learning Framework for Decoding Motor Imagery Tasks of the Same Hand Using EEG Signals

This study aims to increase the control's dimensions of the electroencephalography (EEG)-based brain-computer interface (BCI) systems by distinguishing between the motor imagery (MI) tasks associated with fine body-parts of the same hand, such as the wrist and fingers. This in turn can enable individuals who are suffering from transradial amputations to better control prosthetic hands and to perform various dexterous hand tasks. In particular, we present a novel three-stage framework for decoding MI tasks of the same hand. The three stages of the proposed framework are the input, feature extraction, and classification stages. At the input stage, we employ a quadratic time-frequency distribution (QTFD) to analyze the EEG signals in the joint time-frequency domain. The use of a QTFD enables to transform the EEG signals into a set of two-dimensional (2D) time-frequency images (TFIs) that describe the distribution of the energy encapsulated within the EEG signals in terms of the time, frequency, and electrode position. At the feature extraction stage, we design a new convolutional neural network (CNN) architecture that can automatically analyze and extract salient features from the TFIs created at the input stage. Finally, the features obtained at the feature extraction stage are passed to the classification stage to assign each input TFI to one of the eleven MI tasks that are considered in the current study. The performance of our proposed framework is evaluated using EEG signals that were acquired from eighteen able-bodied subjects and four transradial amputated subjects while performing eleven MI tasks within the same hand. The average classification accuracies obtained for the able-bodied and transradial amputated subjects are 73.7% and 72.8%, respectively. Moreover, our proposed framework yields 14.5% and 11.2% improvements over the results obtained for the able-bodied and transradial amputated subjects, respectively, using conventional QTFD-based handcrafted features and a multi-class support vector machine classifier. The results demonstrate the efficacy of the proposed framework to decode the MI tasks associated with the same hand for able-bodied and transradial amputated subjects.

Time-Frequency Represetation of Radar Signals Using Doppler-Lag Block Searching Wigner-Ville Distribution

Radar signals are time-varying signals where the signal parameters change over time. For these signals, Quadratic Time-Frequency Distribution (QTFD) offers advantages over classical spectrum estimation in terms of frequency and time resolution but it suffers heavily from cross-terms. In generating accurate Time-Frequency Representation (TFR), a kernel function must be able to suppress cross-terms while maintaining auto-terms energy especially in a non-cooperative environment where the parameters of the actual signal are unknown. Thus, a new signal-dependent QTFD is proposed that adaptively estimates the kernel parameters for a wide class of radar signals. The adaptive procedure, Doppler-Lag Block Searching (DLBS) kernel estimation was developed to serve this purpose. Accurate TFRs produced for all simulated radar signals with Instantaneous Frequency (IF) estimation performance are verified using Monte Carlo simulation meeting the requirements of the Cramer-Rao Lower Bound (CRLB) at SNR > 6 dB.

EEG-Based Emotion Recognition Using Quadratic Time-Frequency Distribution.

Accurate recognition and understating of human emotions is an essential skill that can improve the collaboration between humans and machines. In this vein, electroencephalogram (EEG)-based emotion recognition is considered an active research field with challenging issues regarding the analyses of the nonstationary EEG signals and the extraction of salient features that can be used to achieve accurate emotion recognition. In this paper, an EEG-based emotion recognition approach with a novel time-frequency feature extraction technique is presented. In particular, a quadratic time-frequency distribution (QTFD) is employed to construct a high resolution time-frequency representation of the EEG signals and capture the spectral variations of the EEG signals over time. To reduce the dimensionality of the constructed QTFD-based representation, a set of 13 time- and frequency-domain features is extended to the joint time-frequency-domain and employed to quantify the QTFD-based time-frequency representation of the EEG signals. Moreover, to describe different emotion classes, we have utilized the 2D arousal-valence plane to develop four emotion labeling schemes of the EEG signals, such that each emotion labeling scheme defines a set of emotion classes. The extracted time-frequency features are used to construct a set of subject-specific support vector machine classifiers to classify the EEG signals of each subject into the different emotion classes that are defined using each of the four emotion labeling schemes. The performance of the proposed approach is evaluated using a publicly available EEG dataset, namely the DEAPdataset. Moreover, we design three performance evaluation analyses, namely the channel-based analysis, feature-based analysis and neutral class exclusion analysis, to quantify the effects of utilizing different groups of EEG channels that cover various regions in the brain, reducing the dimensionality of the extracted time-frequency features and excluding the EEG signals that correspond to the neutral class, on the capability of the proposed approach to discriminate between different emotion classes. The results reported in the current study demonstrate the efficacy of the proposed QTFD-based approach in recognizing different emotion classes. In particular, the average classification accuracies obtained in differentiating between the various emotion classes defined using each of the four emotion labeling schemes are within the range of –. Moreover, the emotion classification accuracies achieved by our proposed approach are higher than the results reported in several existing state-of-the-art EEG-based emotion recognition studies.

Refining the ambiguity domain characteristics of non-stationary signals for improved time–frequency analysis: Test case of multidirectional and multicomponent piecewise LFM and HFM signals

This paper aims at providing a more accurate description of the ambiguity domain characteristics of a piecewise multicomponent non-stationary signals with focus on piece-wise linear frequency modulated (LFM) (PW-LFM) signal and a mixed LFM and hyperbolic FM (HFM). The main motivation comes from the observed PW-LFM nature of several real life signals. It is essential that the characteristics of these types of signals be taken into account for the design of high resolution Time–Frequency Distributions (TFDs) and therefore to improve the application and interpretation of time–frequency signal analysis and processing. In this paper the ambiguity function (AF) of a general PW-LFM signal is derived exactly and then analyzed to deduce important properties. The precise location and behavior of both auto-terms and cross-terms of a general piecewise LFM signal can be deduced from its AF. Numerical simulations using different types of test signals confirm the analytical derivations. An extension of the PW-LFM test signal is also presented by using HFM signals. For such signals, the exact analytical expression of auto-terms is given as well as the expression of cross-terms between HFM and LFM. The results obtained can be used in future studies to design more advanced quadratic time–frequency distributions (QTFDs) that exhibit improved properties in terms of resolution and accuracy.

Automatic Detection and Classification of Audio Events for Road Surveillance Applications.

This work investigates the problem of detecting hazardous events on roads by designing an audio surveillance system that automatically detects perilous situations such as car crashes and tire skidding. In recent years, research has shown several visual surveillance systems that have been proposed for road monitoring to detect accidents with an aim to improve safety procedures in emergency cases. However, the visual information alone cannot detect certain events such as car crashes and tire skidding, especially under adverse and visually cluttered weather conditions such as snowfall, rain, and fog. Consequently, the incorporation of microphones and audio event detectors based on audio processing can significantly enhance the detection accuracy of such surveillance systems. This paper proposes to combine time-domain, frequency-domain, and joint time-frequency features extracted from a class of quadratic time-frequency distributions (QTFDs) to detect events on roads through audio analysis and processing. Experiments were carried out using a publicly available dataset. The experimental results conform the effectiveness of the proposed approach for detecting hazardous events on roads as demonstrated by 7% improvement of accuracy rate when compared against methods that use individual temporal and spectral features.

A structure for representation of localized time-frequency distributions in presence of noise

This paper considers multi-component non-stationary signals contaminated with additive white Gaussian noise and suggests a structure to remove high noise from quadratic time-frequency distribution (QTFD) of these signals while localizing auto-terms. Proposed structure includes three steps. It first reduces some of the noise power by filtering the distribution in ambiguity domain and thus enhances signal-to-noise ratio. In the second step, the regions corresponding to the auto-terms are determined and by presenting a time-varying threshold, the noise out of auto-terms is eliminated in each time interval. Finally, using reassignment principle, the auto-terms are concentrated to local centroids of their energy. The typical reassignment method localizes both auto-terms and noise components while the proposed procedure relocates only the auto-terms to their original positions. Simulation results illustrate the performance of the proposed structure as compared to more standard state-of-the-art QTFDs.

Time–frequency analysis in infant cry classification using quadratic time frequency distributions

This paper presents a new investigation of time–frequency (t–f) based signal processing approach using quadratic time–frequency distributions (QTFDs) namely spectrogram (SPEC), Wigner–Ville distribution (WVD), Smoothed–Wigner Ville distribution (SWVD), Choi–William distribution (CWD) and modified B-distribution (MBD) for classification of infant cry signals. t–f approaches have proved as an efficient approach for applications involving the non stationary signals. In feature extraction, a cluster of t–f based features were extracted by extending the time-domain and frequency-domain features to the joint t–f domain from the generated t–f representation. Conventional features such as mel-frequency cepstral coefficients (MFCCs) and linear prediction coefficients (LPCs) were also extracted in order to compare the effectiveness of the t–f methods. The efficacy of the extracted feature vectors was validated using probabilistic neural network (PNN) and general regression neural network (GRNN). The proposed methodology was implemented to classify different sets of binary classification problems of infant cry signals from different native. The best empirical result of above 90% was reported and revealed the good potential of t–f methods in the context of infant cry classification.

On the Symplectic Covariance and Interferences of Time-Frequency Distributions

We study the covariance property of quadratic time-frequency distributions with respect to the action of the extended symplectic group. We show how covariance is related to and in fact in competition with the possibility of damping the interferences which arise due to the quadratic nature of the distributions. We also show that the well-known fully covariance property of the Wigner distribution in fact characterizes it (up to a constant factor) among the quadratic distributions $L^{2}(\mathbb{R}^{n})\rightarrow C_{0}({ \mathbb{R}^{2n}})$. A similar characterization for the closely related Weyl transform is given as well. The results are illustrated by several numerical experiments for the Wigner and Born--Jordan distributions of the sum of four Gaussian functions in the so-called diamond configuration.

A robust parameter estimation of FHSS signals using time–frequency analysis in a non-cooperative environment

Frequency hopping spread spectrum (FHSS) signals are widely implemented in both modern civilian and military applications. They are robust to channel impairments because of their low probability of interception. For applications that require the interception of FHSS signals, the signal parameters such as the hopping frequencies, hopping duration and hopping sequence should be accurately measured. In this paper, an accurate FHSS signal parameter estimation method is proposed based on quadratic time–frequency distributions (QTFDs). The extended modified B-distribution (EMBD) and the adaptive smoothed Wigner–Ville (SWWVD) are used which have the properties of high time–frequency resolution. The adaptive SWWVD requires no prior knowledge of the signal parameters since the kernel parameters are estimated from the signal characteristics and are compared to the EMBD which operates at the optimal kernel parameters. The proposed instantaneous frequency (IF) estimate method is compared to the time–frequency (TF) moments method and benchmarked with the Cramer–Rao lower bounds (CRLBs). The computational complexity of the IF estimation method is reduced by a factor of five compared to the TF moments method. Furthermore, the results show that the IF estimation method outperforms moments method where the mean-squared error (MSE) of the hopping frequencies estimate meets at minimum SNR of −3 dB and the hopping duration estimate MSE meets the CRLB at SNR of 0 dB.

Improving DOA Estimation Algorithms Using High-Resolution Quadratic Time-Frequency Distributions

This paper addresses the problem of direction of arrival (DOA) estimation and blind source separation (BSS) for nonstationary signals in the underdetermined case. These two problems are strongly related to the mixing matrix estimation problem. To deal with the nonstationary characteristics of signals, this study uses high-resolution quadratic time-frequency distributions (TFDs) to reduce cross-terms while keeping a good resolution for the construction of spatial TFDs. The main contributions of this paper are two-fold. First, the formulation of a statistical test for the noise thresholding step improves robustness and avoids the use of empirical parameters; this test performs multisource selection of the time-frequency points where the signal of interest is present. Second, an algorithm based on image processing methods performs an auto-source selection for mixing matrix estimation. The results on simulated signals demonstrate an improvement of 10 dB in terms of normalized mean square error for BSS and 7% in terms of relative error for DOA estimation over standard methods.