Given the moments of a time-frequency distribution, one can, in principle, construct the characteristic function from which one then obtains the distribution by Fourier transformation. However, often one can not find ...
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ISBN:
(纸本)9780819468451
Given the moments of a time-frequency distribution, one can, in principle, construct the characteristic function from which one then obtains the distribution by Fourier transformation. However, often one can not find a closed form for the characteristic function and hence one can not obtain the distribution in a direct manner. We formulate the problem of constructing time-frequency representations from moments without first constructing the characteristic function. Our method is based on expanding the distribution in terms of a complete set of functions where the expansion coefficients are dependent directly on the moments. We apply the method to a case where the even moments are manifestly positive which is a necessary condition for obtaining a proper time-frequency representation.
We are presenting a new method for super resolution tracking of frequency modulated sinusoids in white noise. The method is specifically designed to handle the rapid transient problem, i.e. the problem of tracking a c...
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ISBN:
(纸本)9780819468451
We are presenting a new method for super resolution tracking of frequency modulated sinusoids in white noise. The method is specifically designed to handle the rapid transient problem, i.e. the problem of tracking a continuous, rapidly changing instantaneous frequency contour. The proposed method employs to components: 1) an adaptive generalized scale transform 1, 2 which applies a localized change of time-frequency coordinates within the given signal, and 2) an estimation of signal parameters by rotational invariance techniques 3 (ESPRIT). With experiments we have shown that the proposed method provides a significantly higher estimation accuracy than conventional methods. 3 With an optimal choice of transform parameters the estimation error can be reduced dramatically. Error reductions of over 40% have been observed.
We consider the problem of recovering signals from noisy indirect observations under the additional a priori information that the signal is believed to be slowly varying except at all unknown number of points where it...
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ISBN:
(纸本)9780819468451
We consider the problem of recovering signals from noisy indirect observations under the additional a priori information that the signal is believed to be slowly varying except at all unknown number of points where it may have discontinuities of unknown size. The model problem is a linear deconvolution problem. To take advantage of the qualitative prior information available, we use a non-stationary Markov model with the variance of the innovation process also unknown, and apply Bayesian techniques to estimate both the signal and the prior variance. We propose a fast iterative method for computing a MAP estimates and we show that, with a rather standard choices of the hyperpriors, the algorithm produces the fixed point iterative solutions of the total variation and of the Perona-Malik regularization methods. We also demonstrate that, unlike the non-statistical estimation methods, the Bayesian approach leads to a very natural reliability assessment of edge detection by a Markov Chain Monte Carlo (MCMC) based analysis of the posterior.
In this paper, we consider the use of a seismic sensor array for the localization and tracking of a wideband moving source. The proposed solution consists of two steps: source Direction-Of-Arrival (DOA) estimation and...
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ISBN:
(纸本)9780819468451
In this paper, we consider the use of a seismic sensor array for the localization and tracking of a wideband moving source. The proposed solution consists of two steps: source Direction-Of-Arrival (DOA) estimation and localization via DOA estimates. Three DOA estimation methods are considered. The Covariance Matrix Analysis and the Surface Wave Analysis are previously published DOA estimation algorithms shown to be effective in the localization of a stationary wideband source. This paper investigates their performance on moving wideband sources. A novel DOA estimation algorithm, the Modified Kirlin's Method was also developed for the localization of a moving Source. The DOAs estimated by these algorithms are combined rising a least-squares optimization for source localization. The application of these algorithms to real-life data show the effectiveness of both the Surface Wave Analysis and the Modified Kirlin's Method in locating and tracking a wideband moving source.
We discuss the application of time-frequency analysis to biomechanical-type signals, and in particular to signals that would be encountered in the study of rotation rates of bicycle pedaling. We simulate a number of s...
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ISBN:
(纸本)9780819468451
We discuss the application of time-frequency analysis to biomechanical-type signals, and in particular to signals that would be encountered in the study of rotation rates of bicycle pedaling. We simulate a number of such signals and study how well they are represented by various time-frequency methods. We show that time-frequency representations track very well the instantaneous frequency even when there are very fast changes. In addition. we do a correlation analysis between time-series whose instantaneous frequency is changing and show that the traditional correlation coefficient is insufficient to characterize the correlations. We instead show that the correlation coefficient should be evaluated directly from the instantaneous frequencies of the time series, which can be easily estimated from their time-frequency distributions.
An iterative solution is given for solving deblurring problems having nonnegativity constraints through the use of methods motivated by tomographic imaging.
ISBN:
(纸本)0819404098
An iterative solution is given for solving deblurring problems having nonnegativity constraints through the use of methods motivated by tomographic imaging.
In this paper we describe aspects of an ongoing program of work aimed at the practical realization of systolic array structures to implement digital adaptive beam-forming algorithms.
ISBN:
(纸本)0819406945
In this paper we describe aspects of an ongoing program of work aimed at the practical realization of systolic array structures to implement digital adaptive beam-forming algorithms.
We use the Wigner distribution to study pulse propagation in a dispersive media and we show that it leads naturally to a particle view. Using the results obtained we develop a simple approximation method that evolves ...
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ISBN:
(纸本)0819441880
We use the Wigner distribution to study pulse propagation in a dispersive media and we show that it leads naturally to a particle view. Using the results obtained we develop a simple approximation method that evolves a pulse in time.
A new derivation of the QR-based fast recursive least squares algorithms for Toeplitz matrices is presented. algorithms for computing Q and R in the QR decomposition of the data matrix are proposed. These algorithms c...
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ISBN:
(纸本)0819406945
A new derivation of the QR-based fast recursive least squares algorithms for Toeplitz matrices is presented. algorithms for computing Q and R in the QR decomposition of the data matrix are proposed. These algorithms can be efficiently incorporated with the fast recursive least squares algorithm and can be performed only when they are needed.
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