Independent Component Analysis based on Nonparametric Density Estimation on Time-Frequency Domain

Due to the limitation from the uncertainty principle, the window size consistently affects the resolution of time–frequency distributions. Determining the optimal window size is crucial for time–frequency analysis. In this work, we propose the concept of the reliable window width range along time and frequency axes, which simplifies the process of determining the optimal window size and the search range for adaptive methods. Moreover, in existing work, adaptive time–frequency analyses apply either time- or frequency-varying windows. In this study, we utilize a multitaper technique to integrate time- and frequency-varying windows. The proposed concept of the reliable window width range can be applied to any window-based time–frequency analysis method and enhance post-processing methods in the time–frequency plane. Subsequently, together with the reliable window width range, we propose the multitaper adaptive time–frequency windowed synchroextracting transform. It can estimate the optimal window size for time and frequency axes simultaneously and achieve a more energy-concentrated time–frequency analysis result.

Traditional signal postprocessing methods suffer from the repeated assignment problem (RAP), which can result in inaccurate instantaneous frequency (IF) estimation and signal recovery. In this article, to solve this problem, a novel time-frequency (TF) analysis (TFA) method called the synchro-reassigning transform (SRT) is proposed. This method aims to obtain the ideal TF representation (TFR) by utilizing derivatives of the constructed amplitude function and a three-step selection rule to adaptively extract the TF coefficients on the IF trajectories in the TF plane, and reassigning these TF coefficients into a new TFR. In this way, SRT can eliminate the RAP, thus obtaining an approximately ideal TFR that helps to realize more accurate IF estimation and signal reconstruction. Furthermore, SRT shows satisfactory performance on signals with high nonlinear IFs or relatively close IFs, even under strong noise conditions. Two simulated signal and three real-life signals were used to demonstrate the performance of SRT.

A novel underwater target recognition approach has been developed based on the use of Wigner-type Time-Frequency (TF) analysis and the elliptical Gustafson-Kessel (GK) clustering algorithm. This method is implemented for the acoustic backscattered signals of the targets, and more precisely from the examination of echo formation mechanisms in the TF plane. For each of the training signals, we generate a clustering distribution which represents the signal’s TF characteristics by a small number of clusters. A feature template is created by combining the clustering distributions for the signals from the same training target. In the classification process, we calculate the clustering distribution of the test signal and compare it with the feature templates. The target is discriminated in terms of the best match of the clustering pattern. The advantages of GK clustering are that it allows elliptical-shaped clusters, and it automatically adjusts their shapes according to the distribution of the TF feature patterns. The recognition scheme has been applied to discriminate four spherical shell targets filled with different fluids. The data sets are the simulated acoustic responses from these targets, including the interferences caused by the seafloor interaction. [J. A. Fawcett, W. L. J. Fox, and A. Maguer, J. Acoust. Soc. Am. 104, 3296–3304 (1998)]. To evaluate the system robustness, white Gaussian noise is added to the acoustic responses. More than 95% of correct classification is obtained for high Signal-to-Noise Ratio (SNR), and it is maintained around 70% for very low SNRs.

In this paper, we propose a novel method for the detection of road accidents by analyzing audio streams for road surveillance application. In the last decade, due to the increase in a number of people and transportation vehicles, traffic accidents have become one of a major public issue worldwide. The vast number of injuries and death due to road traffic accident reveals the story of a global crisis of road safety. A total of 52,160 road traffic accidents (RTA), 1130 injuries and 85 fatalities were registered during the year 2000, in the state of Qatar. An increase in the number of transportation vehicles around cities has risen the need for more security and safety in public environments. The most obvious reason for a person's death during accidents is the absence or prolong response time of the first aid facility, which is due to the delay in the information of the accident being reached to the police, hospital or ambulance team. In the last couple of years, several surveillance systems have been proposed based on image and video processing for automatically detecting road accidents and car crashes to ensure a quick response by emergency teams. However, in some situations such as adverse weather conditions or cluttered environments, the visual information is not sufficient enough, whereas analyzing the audio tracks can significantly improve the overall reliability of surveillance systems. In this paper we propose a novel method that automatically identifies hazardous situations such as tire skidding and car crashes in presence of background noises, by analyzing the audio streams. Previous studies show that methods for the detection, estimation, and classification of nonstationary signals can be enhanced by utilizing the time-frequency (TF) characteristics of such signals. The TF-based techniques have been proved to outperform classical techniques based on either time or frequency domains, in analyzing real-life nonstationary signals. Time-frequency distributions (TFDs) give additional information about signals that cannot be extracted from either the time domain or frequency domain representations, i.e. the instantaneous frequency of the components of a signal. In order to utilize this extra information provided by TF domain representation, the proposed approach extracts TF image features from quadratic time-frequency distributions (QTFDs), for the detection of audio anomalies. The extended modified-B distribution (EMBD) is utilized to transform a 1-dimensional audio signal into 2-dimensional TF representation which is interpreted as an image. The image descriptors based features are then extracted from the TF representation to classify visually the audio signals into background or abnormal activity patterns in the TF domain. The proposed features are based on Haralick's texture features extracted from the TF representation of audio signals considered and processed as a textured image. These features are used to characterize and hence classify audio signals into M classes. This research study demonstrates that a TF image pattern recognition approach offers significant advantages over standard signal classification methods that utilize either t-domain only or f-domain only features. The proposed method has been experimentally validated on a large open source database of sounds, including several kinds of background noise. The events to be recognized are superimposed on different background sounds of roads and traffic jam. The obtained results are compared with a recent study, utilizing the same large and complex data set of audio signals, and the same experimental setup. The overall classification results confirm the superior performance of the proposed approach with accuracy improvement up to 6%.

Enhanced Cohen class time–frequency methods based on a structure tensor analysis: Applications to ISAR processing

A new feature for the classification of non-stationary signals based on the direction of signal energy in the time–frequency domain

This paper considers the blind separation of nonstationary sources in the underdetermined case, when there are more sources than sensors. A general framework for this problem is to work on sources that are sparse in some signal representation domain. Recently, two methods have been proposed with respect to the time-frequency (TF) domain. The first uses quadratic time-frequency distributions (TFDs) and a clustering approach, and the second uses a linear TFD. Both of these methods assume that the sources are disjoint in the TF domain; i.e., there is, at most, one source present at a point in the TF domain. In this paper, we relax this assumption by allowing the sources to be TF-nondisjoint to a certain extent. In particular, the number of sources present at a point is strictly less than the number of sensors. The separation can still be achieved due to subspace projection that allows us to identify the sources present and to estimate their corresponding TFD values. In particular, we propose two subspace-based algorithms for TF-nondisjoint sources: one uses quadratic TFDs and the other a linear TFD. Another contribution of this paper is a new estimation procedure for the mixing matrix. Finally, then numerical performance of the proposed methods are provided highlighting their performance gain compared to existing ones

In this paper, we introduce a novel independent component analysis (ICA) algorithm, which is truly blind to the particular underlying distribution of the mixed signals. Using a nonparametric kernel density estimation technique, the algorithm performs simultaneously the estimation of the unknown probability density functions of the source signals and the estimation of the unmixing matrix. Following the proposed approach, the blind signal separation framework can be posed as a nonlinear optimization problem, where a closed form expression of the cost function is available, and only the elements of the unmixing matrix appear as unknowns. We conducted a series of Monte Carlo simulations, involving linear mixtures of various source signals with different statistical characteristics and sample sizes. The new algorithm not only consistently outperformed all state-of-the-art ICA methods, but also demonstrated the following properties: 1) Only a flexible model, capable of learning the source statistics, can consistently achieve an accurate separation of all the mixed signals. 2) Adopting a suitably designed optimization framework, it is possible to derive a flexible ICA algorithm that matches the stability and convergence properties of conventional algorithms. 3) A nonparametric approach does not necessarily require large sample sizes in order to outperform methods with fixed or partially adaptive contrast functions.

Time-frequency (TF) analysis (TFA) to nonstationary signals can reveal the nonlinearly changing instantaneous frequencies (IFs) of signals; it is, therefore, widely used for rotating machinery fault diagnosis under time-varying speed conditions. However, the traditional TFA methods may only reveal the outline of IFs due to the extra TF diffusion caused by limited TF resolution, hindering the fault diagnosis of rotating machinery. To enhance the readability of the time-frequency representation (TFR) of the signals with IF trajectories linearly time-varying, linear chirplet transform has been proved effective. To effectively tackle the signal with nonlinearly changing IFs, a string of chirp-rates is preferred, where the final TFR is obtained by superposition of each corresponding sub-TFR at each TF point. However, the extra cross-term interferences resulted from a string of chirp-rates cannot be neglected on TFRs. Aiming at alleviating the cross-terms from the TFR, matching and reassignment based TF enhancement strategy is proposed, where only the appropriate chirp-rate and its corresponding TFR slice is retained at each time instant. The appropriate chirp-rate is adaptively selected by the index—spectral kurtosis. To further increase the readability of the resulting TFR, a reassignment technique synchrosqueezing transform is integrated with the proposed matching strategy. By iteratively employing reassignments, TFR with the enhanced energy and sharp IF ridges can be generated. The effectiveness of the proposed method is validated by both simulated and experimental analyses. It is shown that the proposed method is effective in processing time-varying signals and can provide more accurate IF estimation, which paves the way for rotating machinery fault diagnosis under nonstationary speed conditions.

Refined linear chirplet transform for time–frequency analysis of non-stationary signals

We have been studying relationship between saccadic eye movements and EEG signals. In precious studies, we confirmed sharply changed EEG signals were recorded just before saccade. The EEG signals in right occipital lobe have low potential in the case of saccade to the right side and the EEG signals in left occipital lobe have low potential in the case of saccade to the left side. However, in the previous study, these EEG signals were analyzed in the time-domain. In this research, we analyze saccade-related EEG signals in the time-frequency domain by wavelet transform. As results, we found two patterns of spectrogram in the case of saccade. In the case of eye movements to the left target, a Pattern-1 appeared in the left hemisphere and the other Pattern-2 appeared in the right hemisphere. By contrast, the Pattern-1 appeared in the right hemisphere and the Pattern-2 appeared in the left hemisphere in the case of eye movements to the right target.

Time–frequency analysis and instantaneous frequency estimation using two-sided linear prediction

Estimation of polarization parameters using time–frequency representations and its application to waves separation

Wind turbines usually operate in harsh environments and in working conditions of variable speed, which easily causes their key components such as gearboxes to fail. The gearbox vibration signal of a wind turbine has nonstationary characteristics, and the existing time-frequency (TF) analysis (TFA) methods have some problems such as insufficient concentration of TF energy. In order to obtain a more apparent and more congregated time-frequency representation (TFR), this paper proposes a new TFA method, namely adaptive multiple second-order synchrosqueezing wavelet transform (AMWSST2). Firstly, a short-time window is innovatively introduced on the foundation of classical continuous wavelet transform, and the window width is adaptively optimized by using the center frequency and scale factor. After that, a smoothing process is carried out between different segments to eliminate the discontinuity and thus adaptive wavelet transform is generated. Then, on the basis of the theoretical framework of synchrosqueezing transform and accurate instantaneous frequency estimation by the utilization of second-order local demodulation operator, adaptive second-order synchrosqueezing wavelet transform (AWSST2) is formed. Considering that the quality of actual TFA is greatly disturbed by noise components, through performing multiple synchrosqueezing operations, the congregation of TFR energy is further improved, and finally, the AMWSST2 algorithm studied in this paper is proposed. Since synchrosqueezing operations are performed only in the frequency direction, this method AMWSST2 allows the signal to be perfectly reconstructed. For the verification of its effectiveness, this paper applies it to the processing of the vibration signal of the gearbox of a 750 kW wind turbine.

The combination of recently developed methods for electroencephalographic (EEG) space-time-frequency analysis can provide noninvasive functional neuroimages necessary for obtaining an accurate localization of the epileptogenic zone. The aim of this study was to determine if time-frequency (TF) analysis, followed by EEG source localization, would improve the detection and identification of epileptogenic and related activity. Seventeen patients with refractory frontal lobe epilepsy (FLE) were studied using video EEG recording. TF analysis identified the first epileptogenic EEG changes. Using the Bayesian model averaging (BMA) approach, we compared brain electromagnetic tomographic (BET) images, constructed from the TF domain, with BET images constructed from the time domain only. We determined if the localization identified by BET images was concordant with the localization from medical history and video EEG recording. TF analysis provided a clear display of subtle EEG features, including EEG lateralization, and more concordant and delimited epileptogenic zones, compared with time-domain source analysis. In conclusion, EEG TF analysis improves source localization. After a thorough validation, this methodology could become a useful noninvasive tool for localizing the epileptogenic zone in clinical practice.