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

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

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.

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

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%.

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.

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.

Self-paced learning for instantaneous frequencies estimation in heavy noise environments

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

Decomposition of biomedical signals for enhancement of their time–frequency distributions

The analysis of spectroscopic optical coherence tomography (SOCT) signals suffers the trade-off between time resolution and frequency resolution. Various joint time-frequency distributions (TFDs) can optimize this trade-off. Synthesized signals were generated and experimentally acquired data were obtained to compare and validate several different TFDs under different SOCT imaging schemes. Specific criteria were designed to quantify the TFD performance. We found that different SOCT imaging schemes require different optimal TFDs. Cohen's class TFDs generate the most compact time-frequency (TF) analysis, while linear TFDs offer the most reliable TF analysis. In both cases, if some prior information is known, model-based TF analysis can improve the performance.

A Cohen's class time-frequency (TF) distribution has high resolution in time and frequency simultaneously on a TF plane. It is a powerful tool for nonstationary signal analysis of the type observed commonly in speech and biological signals. A kernel of high resolution was investigated for its applicability to biological signals. To apply the TF analysis with the new kernel to the analysis of a signal from a blood flow, an ultrasound Doppler sinusoidal shift signal was studied. Experimental data were obtained in olive oil by moving a steel ball to and fro by continuously irradiating it with ultrasound. The movement of the steel ball was controlled by various functions. Three kernels were used: (1) a Wigner kernel, (2) a Choi-Williams kernel, and (3) our new kernel. The demodulation accuracy with our new kernel was higher and negative components were smaller than with the Choi-Williams kernel.

The use of linear time-frequency (TF) representa-tions as instantaneous frequency (IF) estimators arises in various fundamental disciplines, mainly thanks to their simplicity and immunity against interfering cross-terms. In this paper, we derive the optimal window width for IF estimation of noisy multicomponent signals based on a family of linear TF transforms that use Gaussian windowing functions and the Fourier oscillatory kernel. Closed-form formulas concerning the estimation bias and the variance are presented, which, thanks to their generality, describe the statistical performance of IF estimators based on transforms with fixed, time-adaptive, frequency-adaptive, or time-frequency adaptive windows. The optimal window is dependent on the unknown first derivative of the IF; therefore, we employ a low-complexity procedure to infer the derivative and optimize the width accordingly. Two adaptive and fully automated TF representations (TFRs) are developed; the first employs a time-adaptive window that minimizes the sum of the mean-squared errors (MSEs) of the IF estimates at each time instant, while in the second TFR, the window is adaptive over time and frequency, minimizing the estimation MSE at each location in the TF domain. Examples using synthetic and real-world signals demonstrate that the proposed algorithms may outperform many popular state-of-the-art techniques, including those that are signal-adaptive, in terms of IF estimation.

A method of range and depth estimation was studied using a single hydrophone based on the dispersive characteristic and time-frequency analysis for low frequency underwater acoustic pulse signals in shallow water environment. First, the signal received on a single hydrophone can be decomposed into a series of modes within the frame work of normal mode theory, and then the dispersive characteristic of the propagating modes can be analyzed using the time-frequency analysis. In order to improve the time-frequency resolution, the use of the time-frequency distribution with adaptive radial-Gaussian kernel extracts the arrival time difference of propagating modes in dispersion curve, which can be used to estimate source range. Mode energy can be extracted using binary time-frequency mask filtering based on multi-mode joint matching processing; and the source depth can be estimated by comparing the differences of the mode energy of the real data and simulated replica data, yielding a contrast function. Simulation results from a shallow-water Pekeris waveguide show that the time-frequency distribution with adaptive radial-Gaussian kernel represents well the dispersion characteristics of the underwater acoustic pulse signals, provides higher time-frequency resolution and overcomes the problem of the inherent limit for the time resolution and frequency resolution in the traditional short-time Fourier transform, so that the modes can be separated and identified more easily in the time-frequency plane. From the result of the range estimation, the different mode combinations have different results of the range estimation. The range estimation result can be obtained accurately by using the mode with high energy in the time-frequency plane. The relative error in range estimation is less than 2% by using the mode with high energy. In terms of the depth estimation, the more the number of joint matching mode, the more sharp peak and low fake peaks the contrast function has, so that the depth estimation is further improved by incorporating more modes. This research has great significance for studying the extraction and separation of low frequency underwater acoustic pulse signals.

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

This paper presents a novel time-frequency (TF) domain nonparametric density estimation independent component analysis (ICA) combined with preprocessing by time-frequency plane Wiener (TFPW) filtering algorithm. It achieves blind separation of over-determined instantaneous linear mixtures of non-stationary sources. The algorithm simultaneously estimates the demixing matrix and the unknown probability density functions of the source signals in TF domain. The proposed method does not require the selection of TF points or TF plane's partition, as the latter is more restrictive to real signals. The TFPW preprocessing improves the algorithm separating effect in noisy data. As simulation shows, it works better than some TF blind separation algorithms