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

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.

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

Linear and bilinear time-frequency distributions (TFDs) have been employed in planetary gearbox fault diagnosis. For linear TFDs, there is a trade-off between the time localization and frequency resolution and the spectrogram may not have correct energy marginals. For bilinear TFDs, they cannot be interpreted as an energy distribution because of the existence of possible negative values even though they are designed for energy density representation. To overcome these shortcomings, TFDs based on copula theory have been reported in the literature. In this paper, we analyze two simulated data sets using linear TFD and copula-based TFD. The results show that the constructed copula-based TFD has desirable properties of being positive, free from cross-term interference, having high time-frequency resolution and matching well with true marginals. The copula-based TFD is also able to locate fault-induced impulses by vertical lines over a certain frequency range in the time-frequency domain. Consequently, this study confirms the advantages of the copula-based TFD as an energy distribution and its capability in fault detection for planetary gearboxes.

Time-Frequency (TF) analyses have been widely used to analyze some nonstationary signals like speech and biological signals. Cohen's class TF distribution has a high resolution in time and frequency and becomes a powerful tool for nonstationary signal analysis. In order to apply the TF analysis using a novel kernel to biological signals, the authors investigated a higher resolution kernel for the ultrasound Doppler signal. The authors would like to apply the TF analysis to blood flow signal analysis. They measured the ultrasound Doppler signal which was obtained in olive oil with a steel ball moving to and fro in the continuous ultrasound. The movement of the steel ball was controlled by various functions. The authors used three kinds of kernel: (1) the Wigner distribution, (2) the Choi-Williams distribution (ED), and (3) the authors' new kernel (named eight figure-kernel), that has high resolution. The results show that the demodulation accuracy with the authors' new kernel is higher and the negative components are smaller than the ED, which makes the cross-term small.

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.

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.

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.

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

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

<p><strong>The natural world is full of sounds produced by plants, animals and even landscape elements. Animals can be incredibly creative in their sound production, and the study of their vocalisation is an essential part of behavioural and conservation ecology. Counting animals' vocalisation is often used as a survey method to monitor population abundances, especially with cryptic or nocturnal species. Once performed only by humans, in the last decades, call counts have evolved, and nowadays, Automatic Recording Units (ARUs) are often used for this purpose, and terabytes of data are collected during acoustics surveys requiring long hours of tedious work to be analysed.</strong></p><p>As a consequence, in recent years, there has been a growing interest in using signal processing and artificial intelligence methods to speed up and facilitate this process.</p><p>Studying sounds, even animal sounds, entails studying how their frequency and intensity change in time, a piece of information not easily readable from the data type collected by ARUs: the waveform. A waveform only describes the change of amplitude with respect to time, but other analysis tools are needed to have information about the instantaneous changes in frequency and intensity.</p><p>In 1946, Koening, Dunn and Lace introduced a 3D representation of sounds, where time, frequency and intensity could be read simultaneously: the spectrogram. The spectrogram, then, became one of the main tools used in the broad field of signal processing and, more specifically, in the study of animal and natural sounds: Bioacoustics. Because the spectrogram combines the representation of a signal in both the time and frequency domain, it is called a Time-Frequency Representation (TFR) of sound.</p><p>However, during these seven decades, more TFRs were introduced to improve the spectrogram, whose performances are hindered by its limits in the time-frequency resolution. Every TFR is defined by a set of parameters that can influence its ability to depict important sound features effectively. Therefore, choosing the best TFR and the best parameters is a challenging task, and it is highly dependent on the characteristics of the sound we are studying. In this thesis, we will explore the differences between the main TFRs present in literature, and we will propose methods to test their performance in some real-world bioacoustics problems involving Aotearoa/New Zealand bats' echolocation data and North Island Brown kiwi calls data. We will also demonstrate how the choice of a TFR and its parameters is crucial if we want to obtain optimal results from our data analysis and discuss the importance of TFRs in Bioacoustics.</p>

Slope synchronous chirplet transform and its application to tacho-less order tracking of rotating machineries

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.

Characterizing in vitro hippocampal ripples using time–frequency analysis