Multi-spectra synchrosqueezing transform

Synchrosqueezing transform (SST) is a high resolution time frequency representation technology for nonstationary signal analysis. The short time Fourier transform-based synchrosqueezing transform (FSST) and the S transform-based synchrosqueezing transform (SSST) time frequency methods are effective tools for bearing fault signal analysis. The fault signals belong to a non-Gaussian and nonstationary alpha (α) stable distribution with 1<α<2 and even the noises being also α stable distribution. The conventional FSST and SSST methods degenerate and even fail under α stable distribution noisy environment. Motivated by the fact that fractional low order STFT and fractional low order S-transform work better than the traditional STFT and S-transform methods under α stable distribution noise environment, we propose in this paper the fractional lower order FSST (FLOFSST) and the fractional lower order SSST (FLOSSST). In addition, we derive the corresponding inverse FLOSST and inverse FLOSSST. The simulation results show that both FLOFSST and FLOSSST perform better than the conventional FSSST and SSST under α stable distribution noise in instantaneous frequency estimation and signal reconstruction. Finally, FLOFSST and FLOSSST are applied to analyze the time frequency distribution of the outer race fault signal. Our results show that FLOFSST and FLOSSST extract the fault features well under symmetric stable (SαS) distribution noise.

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

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.

This study proposes a high-resolution processing technique for seismic data based on the improved synchrosqueezing transform (SST). The SST rearranges the complex spectrum of the wavelet transform along the frequency axis. However, the energy is not concentrated in the position with the faster frequency change rate. To overcome these problems, the proposed method first transformed the seismic signal into an analytical one via Hilbert transformation and then determined the phase correction value (x0(t)) before and after the transformation. This was achieved using the instantaneous frequency attribute (ω(t)) of the analytical signal and a specific frequency (ω0) selected as the dominant frequency of the input data to adjust the change rate of the signal frequency before the SST falls close to zero, which can improve the time–frequency resolution after compression transformation. The essence of this method only adjusts the phase of the signal before and after transformation, without affecting the inverse expression of the SST. The one- and two-dimensional model data results show that the proposed method can better identify the time–frequency distribution characteristics of seismic signals and improve their resolution and the focusing effect in the time–frequency domain. The proposed method shows good prospects for application in gas reservoir detection and identification.

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

Synchrosqueezing transform (SST) benefits from an instantaneous frequency (IF) estimator in the time-frequency domain, providing an energy-concentrated time-frequency representation to describe the time-varying frequency of seismic signals. To enhance the concentration performance of SST, this paper theoretically proposes a statistical SST (SSST) by constructing a spectrum-weighted IF estimator in the short-time Fourier transform (STFT) domain. In this SSST, a linear chirp signal is introduced to better capture its chirp rate, and then the quadratic STFT spectra are weighted by a window-related weighting function. On this basis, two equations related to the IF and chirp rate are constructed to derive the spectrum-weighted IF estimator. Finally, the STFT coefficients are squeezed to the estimated IF trajectories by a frequency fixed-point iterative algorithm, thereby providing a more concentrated time-frequency representation for multi-component signals than existing advanced methods, while enabling to retrieve each component. Two synthetic examples and one field seismic data on thin interbeds are utilized to demonstrate the effectiveness of the proposed SSST and show its ability to highlight the time-varying frequency features of seismic signals, which is a promising seismic data analysis tool, such as characterizing thin interbed thickness variations.

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.

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.

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.

On the use of short-time fourier transform and synchrosqueezing-based demodulation for the retrieval of the modes of multicomponent 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%.

The synchronization of neural activity in the human brain has great significance for coordinating its various cognitive functions. It changes throughout time and in response to frequency. The activity is measured in terms of brain signals, like an electroencephalogram (EEG). The time-frequency (TF) synchronization among several EEG channels is measured in this research using an efficient approach. Most frequently, the windowed Fourier transforms-short-time Fourier transform (STFT), as well as wavelet transform (WT), and are used to measure the TF coherence. The information provided by these model-based methods in the TF domain is insufficient. The proposed synchro squeezing transform (SST)-based TF representation is a data-adaptive approach for resolving the problem of the traditional one. It enables more perfect estimation and better tracking of TF components. The SST generates a clearly defined TF depiction because of its data flexibility and frequency reassignment capabilities. Furthermore, a non-identical smoothing operator is used to smooth the TF coherence, which enhances the statistical consistency of neural synchronization. The experiment is run using both simulated and actual EEG data. The outcomes show that the suggested SST-dependent system performs significantly better than the previously mentioned traditional approaches. As a result, the coherences dependent on the suggested approach clearly distinguish between various forms of motor imagery movement. The TF coherence can be used to measure the interdependencies of neural activities.

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

The Wigner distribution (WD) produces highly concentrated time-frequency (TF) representation of nonstationary signals. It may be used as an efficient signal analysis tool, including the cases of frequency modulated signals corrupted with the Gaussian noise. In some applications, a significant amount of impulse noise is present. Then, the WD fails to produce satisfactory results. The robust periodogram has been introduced for spectral estimation of this kind of noisy signals. It can produce good concentration for pure harmonic signals. However, it is not so efficient in the cases of signals with rapidly varying frequency. This is the motivation for introducing the robust WD. It is a reliable TF representation tool for wide class of nonstationary signals corrupted with impulse noise. This distribution produces good accuracy of the instantaneous frequency (IF) estimation. Using the Huber (1981) loss function, a generalization of the WD is presented. It includes both the standard and the robust WD as special cases. This distribution can be used for TF analysis of signals corrupted with a mixture of impulse and Gaussian noise. The presented theory is illustrated on examples, including applications on the IF estimation and time-varying filtering of signals corrupted with a mixture of the Gaussian and impulse noise. The case study analysis of the IF estimators' accuracy, based on the standard and the robust WD forms, is performed. In order to improve the IF estimation, a median filter is applied on the obtained IF estimate.

Characterizing in vitro hippocampal ripples using time–frequency analysis