Cohen's Class Distributions Research Articles

Seismic data filtering using deconvolutive short-time Fourier transform

Cohen class distributions are well-known time-frequency distributions that have been widely used to analyze different signals. However, they are impractical for signal filtering because they only provide amplitude spectra and suffer from cross terms. In this paper, deconvolutive short-time Fourier transform (DSTFT) is developed by estimating phase spectra and updating moduli to address residual cross terms. The DSTFT moduli is used as weights and apply a weighted least-squares technique to estimate a high-resolution and almost cross-term-free Wigner-Ville distribution. Through numerical tests, it has been found that choosing the optimal window length can minimize cross terms in short-time Fourier transform and DSTFT spectrograms. Furthermore, using thresholding or reweighting techniques can effectively eliminate weights associated with noise. The performance of our method is demonstrated using synthetic and two real seismic wavefield separation problems, including ground-roll removal in seismic shot records and polarization analysis in seismology. The results indicate the high performance of our method in estimating phase spectra and filtering seismic data.

A deep neural network classifier for P300 BCI speller based on Cohen’s class time-frequency distribution

This paper presents a new method of predicting the P300 component of an electroencephalography (EEG)signal to recognize the characters in a P300 brain-computer interface (BCI) speller accurately. This method consistsof a deep learning model and the nonlinear time-frequency features. It is believed that the combination of the deepmodel network and extracting the nonlinear features of the EEG led this research to a better prediction of the P300and, therefore, character recognition. Cohen's class distribution is used in order to extract the nonlinear features of theEEG. Evaluating all of the kernels, Butterworth found to be more informative and it produced better results. Basedon the differences observed between time-frequency responses of target and nontarget signals, specific subbands areselected to extract seven features. A deep-structured neural network, namely stacked sparse autoencoders, is appliedfor BCI character recognition. This deep network reduces the dimension of feature space by extracting unsupervisedfeatures. Then, the features are fed to a Softmax classifier. Afterward, the whole network passes a fine-tuning phase by asupervised backpropagation algorithm. For evaluating the work, Dataset II of BCI Competition III is utilized. Based onthe results, this approach would improve the accuracy in both P300 detection and character recognition. This researchresults in 82.7% and 93.5% accuracy for P300 classification and character recognition, respectively.

On Accumulated Cohen’s Class Distributions and Mixed-State Localization Operators

Recently we introduced mixed-state localization operators associated with a density operator and a (compact) domain in phase space. We continue the investigations of their eigenvalues and eigenvectors. Our main focus is the definition of a time-frequency distribution that is based on the Cohen class distribution associated with the density operator and the eigenvectors of the mixed-state localization operator. This time-frequency distribution is called the accumulated Cohen class distribution. If the trace class operator is a rank-one operator, then the mixed-state localization operators and the accumulated Cohen class distribution reduce to Daubechies’ localization operators and the accumulated spectrogram. We extend all the results about the accumulated spectrogram to the accumulated Cohen class distribution. The techniques used in the case of spectrograms cannot be adapted to other distributions in Cohen’s class since they rely on the reproducing kernel property of the short-time Fourier transform. Our approach is based on quantum harmonic analysis on phase space, which also provides the tools and notions to introduce the analogues of the accumulated spectrogram for mixed-state localization operators, the accumulated Cohen’s class distributions.

Mixed-State Localization Operators: Cohen’s Class and Trace Class Operators

We study mixed-state localization operators from the perspective of Werner’s operator convolutions which allows us to extend known results from the rank-one case to trace class operators. The idea of localizing a signal to a domain in phase space is approached from various directions such as bounds on the spreading function, probability densities associated to mixed-state localization operators, positive operator valued measures, positive correspondence rules and variants of Tauberian theorems for operator translates. Our results include a rigorous treatment of multiwindow-STFT filters and a characterization of mixed-state localization operators as positive correspondence rules. Furthermore we provide a description of the Cohen class in terms of Werner’s convolution of operators and deduce consequences on positive Cohen class distributions, an uncertainty principle, uniqueness and phase retrieval for general elements of Cohen’s class.

О МНОГОМЕРНОМ ПРЕДСТАВЛЕНИИ СИГНАЛОВ АВТОМАТИЧЕСКИХ ДОЗИРУЮЩИХ УСТРОЙСТВ

The article describes the development of a special approach based on using multidimensional wavelet distributions principle to monitor and control the feed dozing processes in the mix preparation unit. As a key component, this approach uses the multidimensional time-frequency Wigner-Ville distribution, which is the part of Cohen's class distributions. The research focuses on signals characterizing mass transfer processes in the form of material flow measuring signals in relevant points of the unit. Wigner-Ville distribution has been shown in time terms as Fourier transform of products of multiplied parts of the signal under consideration for past and future time moments; corresponding distribution for the frequency spectrum is shown as Fourier transform of the products of signal parts for high-frequency and low-frequency fragments of the signal spectrum. It has been noted that when using a complex model of a dozing signal, discrete values (samples) of the latter are considered as its real values. The description of the signal parameters (amplitude, phase, frequency) has been carried out with the help of Hilbert transform. In Cohen's class distributions which represent one-dimensional non-stationary flow signals, the concept of ‘instantaneous frequency’ has been introduced. A graphical explanation for the transformation of a process flow signal from a one-dimensional time domain to a time-frequency 2 D/ 3 D -space is presented. The technology of developing a multidimensional image in the form of Wigner distribution for one-dimensional signals of continuous spiral or screw-type feeders has been examined in detail. There have been considered the features to support Wigner distribution, which allow to guess the presence or absence of time-frequency distribution elements in the interval of signal recording. There has been demonstrated how Wigner distribution can be obtained for a continuous-intermittent feeding signal. It has been concluded that for a certain types of the signal for zero fragments of the latter, non-zero time-frequency elements (i.e. virtual, anomalous ones) appear on the distribution. In addition to Wigner distribution, two other distributions - of Rihachek and Page - are considered. They display the same signal and also contain virtual elements, but in different domains of the time-frequency space. A generalized multidimensional compound signal distribution with a so-called distribution kernel available in it is presented, which includes a correction parameter that allows controlling the intensity of the virtual signal energy.

A Time-Varying Nonparametric Methodology for Assessing Changes in QT Variability Unrelated to Heart Rate Variability.

To propose and test a novel methodology to measure changes in QT interval variability (QTV) unrelated to RR interval variability (RRV) in nonstationary conditions. Time-frequency coherent and residual spectra representing QTV related (QTVrRRV) and unrelated (QTVuRRV) to RRV, respectively, are estimated using time-frequency Cohen's class distributions. The proposed approach decomposes the nonstationary output spectrum of any two-input one-output model with uncorrelated inputs into two spectra representing the information related and unrelated to one of the two inputs, respectively. An algorithm to correct for the bias of the time-frequency coherence function between QTV and RRV is proposed to provide accurate estimates of both QTVuRRV and QTVrRRV. Two simulation studies were conducted to assess the methodology in challenging nonstationary conditions and data recorded during head-up tilt in 16 healthy volunteers were analyzed. In the simulation studies, QTVuRRV changes were tracked with only a minor delay due to the filtering necessary to estimate the nonstationary spectra. The correlation coefficient between theoretical and estimated patterns was even for extremely noisy recordings (signal to noise ratio (SNR) in QTV dB). During head-up tilt, QTVrRRV explained the largest proportion of QTV, whereas QTVuRRV showed higher relative increase than QTV or QTVrRRV in all spectral bands ( for most pairwise comparisons). The proposed approach accurately tracks changes in QTVuRRV. Head-up tilt induced a slightly greater increase in QTVuRRV than in QTVrRRV. The proposed index QTVuRRV may represent an indirect measure of intrinsic ventricular repolarization variability, a marker of cardiac instability associated with sympathetic ventricular modulation and sudden cardiac death.

Exploring laser-driven quantum phenomena from a time-frequency analysis perspective: a comprehensive study.

Time-frequency (TF) analysis is a powerful tool for exploring ultrafast dynamics in atoms and molecules. While some TF methods have demonstrated their usefulness and potential in several quantum systems, a systematic comparison among them is still lacking. To this end, we compare a series of classical and contemporary TF methods by taking hydrogen atom in a strong laser field as a benchmark. In addition, several TF methods such as Cohen class distribution other than the Wigner-Ville distribution, reassignment methods, and the empirical mode decomposition method are first introduced to exploration of ultrafast dynamics. Among these TF methods, the synchrosqueezing transform successfully illustrates the physical mechanisms in the multiphoton ionization regime and in the tunneling ionization regime. Furthermore, an empirical procedure to analyze an unknown complicated quantum system is provided, suggesting the versatility of TF analysis as a new viable venue for exploring quantum dynamics.

Pseudo Cohen Time-Frequency Distributions in Infinite Variance Noise Environment

stable distribution has been suggested as a more appropriate model in impulsive noise environment.The performance of conventional time-frequency distributions (TFDs) degenerate in stable distribution noise environment. Hence, three improved methods are proposed based on Fractional Low Order statistics, Fractional Low Order Wigner-Ville Distribution (FLO-WVD), Fractional Low Order Statistic pseudo Wigner-Ville Distribution (FLO-PWVD), Fractional Low Order Statistic Cohen class distribution (FLO-Cohen). In order for real-time, on-line operation and fairly long signals processing, a new smoothed pseudo Fractional Low Order Cohen class distribution (PFLO-Cohen) is proposed.Simulations show that the methods demonstrate the advantages in this paper, are robust.

A Suitable Hardware Realization for the Cohen Class Distributions

A multidistribution hardware for the realization of the Cohen class distributions is proposed. This approach is based on the modified form of kernel function that is computationally efficient and suitable for real-time implementation. The proposed solution includes various kernels based on the exponential and sine function, with the possibility of choosing different kernel parameters. The proposed architecture is implemented using the field-programmable gate array and can be used in high-speed real-time applications.

Estimation of Time-Varying Coherence and Its Application in Understanding Brain Functional Connectivity

Time-varying coherence is a powerful tool for revealing functional dynamics between different regions in the brain. In this paper, we address ways of estimating evolutionary spectrum and coherence using the general Cohen's class distributions. We show that the intimate connection between the Cohen's class-based spectra and the evolutionary spectra defined on the locally stationary time series can be linked by the kernel functions of the Cohen's class distributions. The time-varying spectra and coherence are further generalized with the Stockwell transform, a multiscale time-frequency representation. The Stockwell measures can be studied in the framework of the Cohen's class distributions with a generalized frequency-dependent kernel function. A magnetoencephalography study using the Stockwell coherence reveals an interesting temporal interaction between contralateral and ipsilateral motor cortices under the multisource interference task.

Phase-space representation of partially coherent imaging systems using the Cohen class distribution

We develop a phase-space representation (termed phase-space imager) suitable for analysis and design of imaging systems that use large illumination apertures (partially coherent illumination). The representation, developed from the transmission cross-coefficient model, falls in the general Cohen class of distributions and elegantly captures the bilinear nature of image formation in partially coherent systems. It uses only the requisite number of dimensions and leads to an efficient algorithm for calculating images. Computed partially coherent images of a double slit and a two-dimensional sinusoidal spoke are presented.

Estimation of modal parameters using bilinear joint time–frequency distributions

In this paper, a new method is proposed for modal parameter estimation using time–frequency representations. Smoothed Pseudo Wigner–Ville distribution which is a member of the Cohen's class distributions is used to decouple vibration modes completely in order to study each mode separately. This distribution reduces cross-terms which are troublesome in Wigner–Ville distribution and retains the resolution as well. The method was applied to highly damped systems, and results were superior to those obtained via other conventional methods.

Double-dimensional distributions: another approach to "quartic" distributions

We present the definitions of double-dimensional time-frequency distributions, especially the Wigner distribution (WD) of the WD and the ambiguity function of the ambiguity function. The first coincides with the notion of the local ambiguity function presented in the papers of O'Neill and Williams (1999), and O'Neill and Flandrin (2000) and are classified as the time-frequency distribution. The second turned out to be the Fourier transform of the quartic ambiguous ambiguity function. Using the above notions, the double dimensional extension of the Cohen's class distributions is defined and illustrated by examples.

Multi-scale representation of tribological surfaces

Many numerical surface topography analysis methods exist today. However, even for the moderately complicated topography of a tribological surface these methods can provide only limited information. The reason is that tribological surfaces often exhibit a non-stationary and multi-scale nature while the numerical methods currently used work well with surface data exhibiting a stationary random process and provide surface descriptors closely related to a scale at which surface data were acquired. The suitability of different methods, including Fourier transform, windowed Fourier transform, Cohen's class distributions (especially the Wigner-Ville distribution), wavelet transform, fractal methods and a hybrid fractal-wavelet method, for the analysis of tribological surface topographies is investigated in this paper. The method best suited to this purpose has been selected.

THE ANALYSIS OF NON-STATIONARY SIGNALS USING TIME-FREQUENCY METHODS

This paper deals with the time–frequency analysis of deterministic and stochastic non-stationary signals. It includes the following: a brief review of the fundamentals of time–frequency analysis and various time–frequency distributions; a summary of the inter-relations between time–frequency distributions, emphasizing links between evolutionary spectra, the Wigner-Ville distribution, and Cohen-class distribution; demonstration of the effects of using different analysis methods on sample time histories; the analytical modelling of physical phenomena so as to predict theoreticaltime-frequency distributions, with a view to offering insight into the signal generation mechanisms.

Matching pursuits with time-frequency dictionaries

The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions. These waveforms are chosen in order to best match the signal structures. Matching pursuits are general procedures to compute adaptive signal representations. With a dictionary of Gabor functions a matching pursuit defines an adaptive time-frequency transform. They derive a signal energy distribution in the time-frequency plane, which does not include interference terms, unlike Wigner and Cohen class distributions. A matching pursuit isolates the signal structures that are coherent with respect to a given dictionary. An application to pattern extraction from noisy signals is described. They compare a matching pursuit decomposition with a signal expansion over an optimized wavepacket orthonormal basis, selected with the algorithm of Coifman and Wickerhauser see (IEEE Trans. Informat. Theory, vol. 38, Mar. 1992).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>