STFATool: A Sparse Time–Frequency Analysis Toolkit for non-stationary signals

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) 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.

Time–frequency analysis based on Vold-Kalman filter and higher order energy separation for fault diagnosis of wind turbine planetary gearbox under nonstationary conditions

Time–frequency analysis of tribological systems—part I: implementation and interpretation

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.

This paper explores three groups of time–frequency distributions: the Cohen’s, affine, and reassigned classes of time–frequency representations (TFRs). This study provides detailed insight into the theory behind the selected TFRs belonging to these classes. Extensive numerical simulations were performed with examples that illustrate the behavior of the analyzed TFR classes in the joint time–frequency domain. The methods were applied both on synthetic and real-life non-stationary signals. The obtained results were assessed with respect to time–frequency concentration (measured by the Rényi entropy), instantaneous frequency (IF) estimation accuracy, cross-term presence in the TFRs, and the computational cost of the TFRs. This study gives valuable insight into the advantages and limitations of the analyzed TFRs and assists in selecting the proper distribution when analyzing given non-stationary signals in the time–frequency domain.

The vibration generated by industrial machines always contains nonlinear and non-stationary signals. It is expected that a desired time-frequency analysis method should have good computation efficiency, and have good resolution in both time domain and frequency domain. In this paper, the adaptive Gaussian chirplet distribution for an integrated time-frequency signature extraction of the machine vibration is presented. The adaptive Gaussian chirplet spectrogram is non-negative, has a high time-frequency resolution, and is free of cross term interference, so it offers the advantage of good localization of the vibration signal energy in the time-frequency domain. Experimental results show that the proposed method is very effective.

Time-varying demodulation analysis for rolling bearing fault diagnosis under variable speed conditions

Multi-scale chirplet synchroextracting transform for accurate characterization of adjacent fault features in rotating machinery

Modern radars use complex waveforms to obtain high detection performance and low probabilities of interception and identification. Signals intercepted from multiple radars overlap considerably in both the time and frequency domains and are difficult to separate with primary time parameters. Time–frequency analysis (TFA), as a key signal-processing tool, can provide better insight into the signal than conventional methods. In particular, among the various types of TFA, parameterized time-frequency analysis (PTFA) has shown great potential to investigate the time–frequency features of such non-stationary signals. In this paper, we propose a procedure for PTFA to separate overlapped radar signals; it includes five steps: initiation, parameterized time-frequency analysis, demodulating the signal of interest, adaptive filtering and recovering the signal. The effectiveness of the method was verified with simulated data and an intercepted radar signal received in a microwave laboratory. The results show that the proposed method has good performance and has potential in electronic reconnaissance applications, such as electronic intelligence, electronic warfare support measures, and radar warning.

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.

Time-varying filtering for nonstationary signal analysis of rotating machinery: Principle and applications

Parkinson’s Disease (PD) is a neurodegenerative disease, which is becoming an increasingly greater social issue due to the growing incidence rate caused by population ageing. Over the recent years, the doctors have been focusing on searching for new methods supporting the diagnosis of such disorders. Acoustic voice analysis in Parkinson’s patients can be a valuable and objective tool supporting the diagnosing diseases of neurodegenerative nature. The article discusses a concept of utilizing voice processing techniques in evaluating patients with Parkinson’s disease. Using time analysis, frequency analysis and time-frequency analysis, the authors attempted performing acoustic voice analysis in that group of patients. The research utilized recordings conducted at the Department of Neurology at the Medical University of Warsaw. The study involved both women and men. The recording scenario was divided into several parts. The first part contained two various texts read out by the tested person. Yet another segment involved recording the vowel “a” with prolonged phonation, uttered by a patient for at least 5 seconds. The last part of the recordings involved the patient uttering individual words and sentences according to an assumed scenario. A total of 7 acoustic signals per patient, with an average length of ca. 75 seconds were recorded. The conclusions from the conducted studies will enable determining, which of the applied techniques can be a promising tool for supporting the diagnostics of neurodegenerative disorders, including parkinsonism. Further studies involving larger groups are required in order to confirm the obtained results and the structure of a target diagnostic system.

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 many applications, it may be desired to decompose a non‐stationary signal into its individual components. If spectral components of the non‐stationary signal do not overlap in the frequency domain then Fourier transform can be used to decompose the non‐stationary signal. Fourier transform fails to decompose the non‐stationary signal if its spectral components overlap in the frequency domain. In this study, the authors propose Fourier‐Bessel transform and the time–frequency analysis in conjunction with the fractional Fourier transform (FB‐TF) method for the separation of multi‐component non‐stationary signal whose components overlap in both time and/or frequency domains. The efficiency of the proposed method is compared with one of the traditional decomposition methods like EMD. The proposed approach is applied to both simulated and experimental radar data. Results demonstrate the effectiveness of the proposed method for non‐stationary signal separation and for detecting manoeuvring target in heavy sea‐clutter environments. The improvement factor and clutter attenuation are calculated and used to compare the performance of the EMD and the FB‐TF methods in suppressing the sea‐clutter and enhancing target detection. The proposed method can be used as a potential tool for detecting and enhancing the low observable manoeuvring air targets in the sea‐clutter environment.