Time-frequency analysis with eight-figure kernel

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.

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

The local Wigner-Ville distribution (LWVD) extends the Cohen's class time-frequency distributions (TFD) by the definition of a kernel for each time-frequency point (local kernel). The subject of the paper is the determination of these local kernels for interference reduction. Starting from the simple idea of the local limitation of the Wigner-Ville TFD integral bounds, a method is presented to estimate these limits and to obtain a reduced interference TFD. The effectiveness for interference reduction of this LWVD, especially when compared to global-kernel methods, is shown using example signals.

Doppler signals from a disturbed arterial blood flow are very likely to be nonstationary for they usually have a time-varying frequency structure caused by a complicated flow pattern. Therefore conventional Fourier analysis based methods are unsuitable for this application. This paper introduces the application of joint time-frequency analysis (TFA) to estimate the frequency dynamics of arterial Doppler blood flow signals and to detect the presence of small stenoses of the artery. The short time Fourier transform (STFT), Wigner distribution (WD), and Choi-Williams distribution (CWD) were investigated. The results of synthetic signal analysis show that the STFT, WD and CWD follow the transient changes of frequency well, and the STFT and CWD also behave well for multicomponent signals. Doppler spectra were obtained by means of the FFT, STFT, WD, and CWD for different flow rates and positions along a simulated blood vessel for stenoses ranging from 2% to 25% cross sectional area reduction (CSAR) using a blood analogue. The results indicate that all of these methods are to some extent capable of detecting stenoses as small as 2% CSAR by identifying the existence of negative frequency components in the spectra, and the CWD appears at this stage to be superior to the STFT and WD.

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%.

This thesis proposes new, efficient techniques for implementing some members of the Hyperbolic class of time-frequency distributions (TFD). A new, efficient algorithm is proposed for the Altes-Marinovic Q-distribution. The algorithm is a generalization of the Fast Mellin transform implementation of the Bertrand P0 distribution. Other TFDs of the Hyperbolic class, which are the smoothed versions of the Altes-Marinovic distribution, are implemented using Fast Mellin transform to compute the Altes distribution of the signal, which is then appropriately weighted and smoothed using numerical integration and first order linear interpolation techniques. Also, an extensive analysis of the warping technique proposed by Canfield and Jones is done in this thesis. Canfield and Jone have implemented the data adaptive, radially Gaussian kernel hyperbolic class time-frequency representation. We have used their warping technique but the different kernels to implement various members of the Hyperbolic class like the Pseudo Altes-Marinovic distribution, Smoothed Pseudo Altes-Marinovic distribution, etc. Our implementation has the following approach. The Woodward Ambiguity function of the logarithmically frequency warped signal is calculated to compute the Hyperbolic ambiguity function. The Hyperbolic ambiguity function (HAF) is examined to determine the mapping of the various signal auto and cross components. Many complicated signals map to simple regions in the HAF plane. A suitable kernel is chosen so as to remove the cross terms without distorting the auto terms and is multiplied with the Hyperbolic Ambiguity function. Since HC class kernels can be formulated to be equivalent to (up to a proportionality factor) Cohen's class kernels, all of the useful kernel design strategies this far developed for Cohen's class TFDs can now be applied straight forwardly to HAF plane kernel design. Then, a two dimensional Fourier transform of the product is taken. The time frequency localization of the result is corrected to compute the corresponding hyperbolic class time frequency distribution. This approach is intuitive and often makes kernel design easier for cross term removal. The logarithmic signal spectrum warping and the time frequency localization are implemented using the warpings techniques proposed by Canfield and Jones. Also, a new Hyperbolic class member is proposed which uses the Multiform tiltable exponential kernel of Costa in the Hyperbolic Ambiguity function domain. This kernel does as wells as or better than other Hyperbolic class TFDs in time-frequency scenarios that were considered in this thesis. Various nonstationary signals like Hyperbolic impulses, linear FM chirps, etc. were analyzed. In the case of Hyperbolic impulses,

In the course of this study, time-frequency energy distribution techniques have been compared using a series of test signals that have very specific profiles in the time frequency domain. The techniques, which are going to be examined are the short time Fourier transform, wavelet transform, Wigner-Ville transform, pseudo Wigner-Ville distribution, Rihaczek and Margenau Hill distributions, smoothed pseudo Wigner-Ville distribution, Choi-Williams distribution, Born-Jordan distribution, Zhao Atlas Marks distribution and Baranuik Jones optimal radially Gaussian kernel method. These techniques are all a subset of the Cohen class of energy distributions. In order to examine these techniques, three test signals were used. The first signal is two chirp signals, one increasing in frequency and the other decreasing in frequency. This signal ideally should have a distinctive "X" shape in the time-frequency domain. The second signal is an amplitude-modulated signal with two added impulses. This ideally should have an "U" shape in the time frequency domain. The final signal is the linear sum of the two signals as explained above. An ideal time frequency representation for the three signals was generated and a comparison between the techniques was taken against these ideal signals using percentile root mean squared differences. These signals are among the most difficult signals to resolve in the time-frequency domain.

Simulation studies of Doppler ultrasound blood flow signals from intracranial aneurysms in a pulsatile flow can provide a useful guidance for detecting the formation and growth progress of the intracranial aneurysms using the Doppler ultrasound technology and forecasting the size of aneurysm. Firstly, blood flow velocity distribution in the area of Intracranial aneurysm is calculated by solving the Navier-Stokes equations. Secondly, power spectral density (PSD) of the Doppler signals is estimated by summing the contribution of all scatterers through the vessel radius divided into elemental radius. Finally, the Doppler ultrasound blood flow signals are simulated using the cosine summation method. The model generates Doppler blood flow signals with the characteristics similar to those found in practice. The results show that the proposed approach is useful for simulating Doppler ultrasound signals from intracranial aneurysms in a pulsatile flow.

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

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.

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.

The Wigner distribution is a milestone of Time–frequency Analysis. In order to cope with its drawbacks while preserving the desirable features that made it so popular, several kinds of modifications have been proposed. This contribution fits into this perspective. We introduce a family of phase-space representations of Wigner type associated with invertible matrices and explore their general properties. As a main result, we provide a characterization for the Cohen’s class [L. Cohen, Generalized phase-space distribution functions, J. Math. Phys. 7 (1996) 781–786; Time–frequency Analysis (Prentice Hall, New Jersey, 1995)]. This feature suggests to interpret this family of representations as linear perturbations of the Wigner distribution. We show which of its properties survive under linear perturbations and which ones are truly distinctive of its central role.

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

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.