Wigner-Ville spectral analysis of nonstationary processes
01 Dec 1985-IEEE Transactions on Acoustics, Speech, and Signal Processing (IEEE)-Vol. 33, Iss: 6, pp 1461-1470
TL;DR: A general class of spectral estimators of the Wigner-Ville spectrum is proposed: this class is based on arbitrarily weighted covariance estimators and its formal description corresponds to the generalclass of conjoint time-frequency representations of deterministic signals with finite energy.
Abstract: The Wigner-Ville spectrum has been recently introduced as the unique generalized spectrum for time-varying spectral analysis. Its properties are revised with emphasis on its central role in the analysis of second-order properties of nonstationary random signals. We propose here a general class of spectral estimators of the Wigner-Ville spectrum: this class is based on arbitrarily weighted covariance estimators and its formal description corresponds to the general class of conjoint time-frequency representations of deterministic signals with finite energy. Classical estimators like short-time periodograms and the recently introduced pseudo-Wigner estimators are shown to be special cases of the general class. The generalized framework allows the calculation of the moments of general spectral estimators and comparing the results emphasizes the versatility of the new pseudo-Wigner estimators. The effective numerical implementation, by an N-point FFT, of pseudo-Wigner estimators of 2N points is indicated and various examples are given.
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Book•
01 Jan 1998
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
Abstract: Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.
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TL;DR: A review and tutorial of the fundamental ideas and methods of joint time-frequency distributions is presented with emphasis on the diversity of concepts and motivations that have gone into the formation of the field.
Abstract: A review and tutorial of the fundamental ideas and methods of joint time-frequency distributions is presented. The objective of the field is to describe how the spectral content of a signal changes in time and to develop the physical and mathematical ideas needed to understand what a time-varying spectrum is. The basic gal is to devise a distribution that represents the energy or intensity of a signal simultaneously in time and frequency. Although the basic notions have been developing steadily over the last 40 years, there have recently been significant advances. This review is intended to be understandable to the nonspecialist with emphasis on the diversity of concepts and motivations that have gone into the formation of the field. >
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TL;DR: A tutorial review of both linear and quadratic representations is given, and examples of the application of these representations to typical problems encountered in time-varying signal processing are provided.
Abstract: A tutorial review of both linear and quadratic representations is given. The linear representations discussed are the short-time Fourier transform and the wavelet transform. The discussion of quadratic representations concentrates on the Wigner distribution, the ambiguity function, smoothed versions of the Wigner distribution, and various classes of quadratic time-frequency representations. Examples of the application of these representations to typical problems encountered in time-varying signal processing are provided. >
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TL;DR: In this article, a time-frequency distribution of L. Cohen's (1966) class is introduced, which is called exponential distribution (ED) after its exponential kernel function, and the authors interpret the ED from the spectral density-estimation point of view.
Abstract: The authors introduce a time-frequency distribution of L. Cohen's (1966) class and examines its properties. This distribution is called exponential distribution (ED) after its exponential kernel function. First, the authors interpret the ED from the spectral-density-estimation point of view. They then show how the exponential kernel controls the cross terms as represented in the generalized ambiguity function domain, and they analyze the ED for two specific types of multicomponent signals: sinusoidal signals and chirp signals. Next, they define the ED for discrete-time signals and the running windowed exponential distribution (RWED), which is computationally efficient. Finally, the authors present numerical examples of the RWED using the synthetically generated signals. It is found that the ED is very effective in diminishing the effects of cross terms while retaining most of the properties which are useful for a time-frequency distribution. >
1,306 citations
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Abstract: Electromyography (EMG) signals can be used for clinical/biomedical applications, Evolvable Hardware Chip (EHW) development, and modern human computer interaction. EMG signals acquired from muscles require advanced methods for detection, decomposition, processing, and classification. The purpose of this paper is to illustrate the various methodologies and algorithms for EMG signal analysis to provide efficient and effective ways of understanding the signal and its nature. We further point up some of the hardware implementations using EMG focusing on applications related to prosthetic hand control, grasp recognition, and human computer interaction. A comparison study is also given to show performance of various EMG signal analysis methods. This paper provides researchers a good understanding of EMG signal and its analysis procedures. This knowledge will help them develop more powerful, flexible, and efficient applications.
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Cites background from "Wigner-Ville spectral analysis of n..."
...Previous works by Martin and Flandrin ( 24 ), Amin (25) and Syeed and Jones (26) demonstrated that any Cohen class time-frequency spectrum S(t,f) may be written as equation 5:...
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References
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TL;DR: In this article, the Boltzmann formula for the probability of a configuration is given in classical theory by means of a probability function, and the result discussed is developed for the correction term.
Abstract: The probability of a configuration is given in classical theory by the Boltzmann formula $\mathrm{exp}[\ensuremath{-}\frac{V}{\mathrm{hT}}]$ where $V$ is the potential energy of this configuration. For high temperatures this of course also holds in quantum theory. For lower temperatures, however, a correction term has to be introduced, which can be developed into a power series of $h$. The formula is developed for this correction by means of a probability function and the result discussed.
6,791 citations
TL;DR: In this article, the Boltzmann formula for lower temperatures has been developed for a correction term, which can be developed into a power series of h. The formula is developed for this correction by means of a probability function and the result discussed.
Abstract: The probability of a configuration is given in classical theory by the Boltzmann formula exp [— V/hT] where V is the potential energy of this configuration. For high temperatures this of course also holds in quantum theory. For lower temperatures, however, a correction term has to be introduced, which can be developed into a power series of h. The formula is developed for this correction by means of a probability function and the result discussed.
5,865 citations
Journal Article•
21 Mar 1991
TL;DR: In this article, the authors introduce the concept of Stationary Random Processes and Spectral Analysis in the Time Domain and Frequency Domain, and present an analysis of Processes with Mixed Spectra.
Abstract: Preface. Preface to Volume 2. Contents of Volume 2. List of Main Notation. Basic Concepts. Elements of Probability Theory. Stationary Random Processes. Spectral Analysis. Estimation in the Time Domain. Estimation in the Frequency Domain. Spectral Analysis in Practice. Analysis of Processes with Mixed Spectra.
5,238 citations
TL;DR: In this paper, it was shown that instead of Wigner's approximation, instead of the classical potential U in the exponent by U-kTf, where f is the same as Wigneer's function, the probability of any configurational position is then proportional to exp −U/kT, with U the potential energy.
Abstract: The behavior of any system at high enough temperatures approaches that of its classical counterpart. The probability of any configurational position is then proportional to exp—U/kT, with U the potential energy. Wigner has shown that quantum‐mechanical deviations, as the temperature is lowered, may be approximated by multiplication of this with 1–f, where f is a function proportional to h2 and having terms in T−2 and terms in T−3. This type of approximation is unsatisfactory for a system of many degrees of freedom, that is, one of many dependent molecules. For such a system it is shown that instead of Wigner's approximation we may replace the classical potential U in the exponent by U—kTf, where f is the same as Wigner's function.
1,968 citations
TL;DR: In this article, a set of quasi-probability distribution functions which give the correct quantum mechanical marginal distributions of position and momentum is studied, and a general relationship between the phase-space distribution functions and the rule of associating classical quantities to quantum mechanical operators is derived.
Abstract: A set of quasi-probability distribution functions which give the correct quantum mechanical marginal distributions of position and momentum is studied. The phase-space distribution does not have to be bilinear in the state function. The Wigner distribution is a special case. A general relationship between the phase-space distribution functions and the rule of associating classical quantities to quantum mechanical operators is derived. This allows the writing of correspondence rules at will, of which the ones presently known are particular cases. The dynamics and other properties of the generalized phase-space distribution are considered.
1,092 citations