The Experts below are selected from a list of 129 Experts worldwide ranked by ideXlab platform
Alfred Hanssen - One of the best experts on this subject based on the ideXlab platform.
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a geometric interpretation of the Rihaczek time frequency Distribution for stochastic signals
International Symposium on Information Theory, 2005Co-Authors: Peter J. Schreier, Louis L. Scharf, Alfred HanssenAbstract:Based on the Cramer-Loeve spectral representation for a harmonizable random process, the Rihaczek Distribution is a time- and frequency-shift covariant, bilinear time-frequency Distribution. It can be expressed as a complex Hilbert space inner product between the time series and its infinitesimal stochastic Fourier generator. We show that we may attach an illuminating geometry to this inner product, wherein the cosine-squared of the angle between the time series and its infinitesimal stochastic Fourier generator is given by the Rihaczek Distribution. We propose to construct estimators of the Rihaczek Distribution using a factored kernel in Cohen's class of bilinear time-frequency Distributions
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The Hilbert space geometry of the Rihaczek Distribution for stochastic analytic signals
IEEE Signal Processing Letters, 2005Co-Authors: Louis L. Scharf, Peter J. Schreier, Alfred HanssenAbstract:The Rihaczek Distribution for stochastic signals is a time- and frequency-shift covariant bilinear time-frequency Distribution (TFD) based on the Crame/spl acute/r-Loe/spl grave/ve spectral representation for a harmonizable process. It is a complex Hilbert space inner product (or cross correlation) between the time series and its infinitesimal stochastic Fourier generator. To this inner product, we may attach an illuminating geometry, wherein the cosine squared of the angle between the time series and its infinitesimal stochastic Fourier generator is given by the Rihaczek Distribution. The Rihaczek Distribution also determines a time-varying Wiener filter for estimating a time series from its infinitesimal stochastic Fourier generator and measures the resulting error covariance. We propose a factored kernel to construct estimators of the Rihaczek Distribution that are contained in Cohen's class of bilinear TFDs.
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ISIT - A geometric interpretation of the Rihaczek time-frequency Distribution for stochastic signals
Proceedings. International Symposium on Information Theory 2005. ISIT 2005., 2005Co-Authors: Peter J. Schreier, Louis L. Scharf, Alfred HanssenAbstract:Based on the Cramer-Loeve spectral representation for a harmonizable random process, the Rihaczek Distribution is a time- and frequency-shift covariant, bilinear time-frequency Distribution. It can be expressed as a complex Hilbert space inner product between the time series and its infinitesimal stochastic Fourier generator. We show that we may attach an illuminating geometry to this inner product, wherein the cosine-squared of the angle between the time series and its infinitesimal stochastic Fourier generator is given by the Rihaczek Distribution. We propose to construct estimators of the Rihaczek Distribution using a factored kernel in Cohen's class of bilinear time-frequency Distributions
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EUSIPCO - Complex time-frequency and dual-frequency spectra of harmonizable processes
2004Co-Authors: Alfred Hanssen, Y. Larsen, Louis L. ScharfAbstract:Harmonizable processes form a huge and useful class of nonstationary random processes. In this paper, we will discuss the properties of, and some consequences of employing a natural choice of complex valued densities to characterize the harmonizable class. In particular, we will discuss the Hilbert space geometry of the resulting complex time-frequency description (related to the Rihaczek Distribution), and the dual-frequency description (related to the Loeve spectrum). We will demonstrate that useful normalized nonstationary generalizations of coherence emerge from this picture. Finally, we extend the formalism to random fields and to higher-order
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ICASSP - Theory of higher-order Rihaczek spectra
IEEE International Conference on Acoustics Speech and Signal Processing, 2002Co-Authors: Alfred Hanssen, Loui L. ScharfAbstract:The Rihaczek Distribution was originally proposed as a second-order complex valued time-frequency correlation function for energy signals. In this paper, we show that the generalization to higher orders and to stochastic processes arises naturally from considerations of the nonstationary moment functions. These so-called higher-order Rihaczek spectra (HORS) are shown to exhibit many interesting, important, and desirable properties as measures of the time and frequency behavior of stochastic processes. We show that the n-th order HORS is to be interpreted as the Distribution of complex correlation between a stochastic process and an (n − 1) dimensional (multifrequency) random field. Under stationarity assumptions, we found that the HORS collapses to the conventional stationary moment spectrum. The frequency and time marginals of the n-th order are the n-th order instantaneous moment, and the n-th order stationary moment spectrum, respectively. Finally, we evaluated the n-th order HORS for the output process from a nonstationary channel excited by a white, stationary, and non-Gaussian source, and we found that all orders of the HORS contain useful information about the time-frequency behavior of the channel.
Selin Aviyente - One of the best experts on this subject based on the ideXlab platform.
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Time-Frequency Based Phase-Amplitude Coupling Measure For Neuronal Oscillations
Scientific Reports, 2019Co-Authors: Tamanna T. K. Munia, Selin AviyenteAbstract:Oscillatory activity in the brain has been associated with a wide variety of cognitive processes including decision making, feedback processing, and working memory. The high temporal resolution provided by electroencephalography (EEG) enables the study of variation of oscillatory power and coupling across time. Various forms of neural synchrony across frequency bands have been suggested as the mechanism underlying neural binding. Recently, a considerable amount of work has focused on phase-amplitude coupling (PAC)– a form of cross-frequency coupling where the amplitude of a high frequency signal is modulated by the phase of low frequency oscillations. The existing methods for assessing PAC have some limitations including limited frequency resolution and sensitivity to noise, data length and sampling rate due to the inherent dependence on bandpass filtering. In this paper, we propose a new time-frequency based PAC (t-f PAC) measure that can address these issues. The proposed method relies on a complex time-frequency Distribution, known as the Reduced Interference Distribution (RID)-Rihaczek Distribution, to estimate both the phase and the envelope of low and high frequency oscillations, respectively. As such, it does not rely on bandpass filtering and possesses some of the desirable properties of time-frequency Distributions such as high frequency resolution. The proposed technique is first evaluated for simulated data and then applied to an EEG speeded reaction task dataset. The results illustrate that the proposed time-frequency based PAC is more robust to varying signal parameters and provides a more accurate measure of coupling strength.
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A Time-Frequency-Based Approach to Phase and Phase Synchrony Estimation
IEEE Transactions on Signal Processing, 2011Co-Authors: Selin Aviyente, Ali Yener MutluAbstract:Time-varying phase synchrony is an important bivariate measure that quantifies the dynamics between nonstationary signals and has been widely used in many applications including chaotic oscillators in physics and multichannel electroencephalography recordings in neuroscience. Current state-of-the-art in time-varying phase estimation uses either the Hilbert transform or the complex wavelet transform of the signals. Both of these methods have some major drawbacks such as the assumption that the signals are narrowband for the Hilbert transform and the nonuniform time-frequency resolution inherent to the wavelet analysis. In this paper, a new phase estimation method based on the Rihaczek Distribution and Reduced Interference Rihaczek Distribution belonging to Cohen's class is proposed. These Distributions offer phase estimates with uniformly high time-frequency resolution which can be used for defining time and frequency dependent phase synchrony. Properties of the phase estimator and the corresponding phase synchrony measure are evaluated both analytically and through simulations showing the effectiveness of the new measures compared to existing methods.
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Comparison of nonparametric and parametric time-varying methods for quantifying phase synchrony
2010 Conference Record of the Forty Fourth Asilomar Conference on Signals Systems and Computers, 2010Co-Authors: Ali Yener Mutlu, Selin AviyenteAbstract:Quantifying the pairwise relationships between two signals is an important problem in many fields of science and engineering. Phase synchrony has been suggested as a powerful tool for determining bivariate signal relationships. Recently, a nonparametric phase estimation method based on the Rihaczek Distribution belonging to Cohen's class of time-frequency Distributions (TFDs) has been proposed for the estimation of time-varying phase [1]. Alternatively, parametric time-frequency methods, which model the phase as a polynomial, can be used. In this paper, the nonparametric phase estimator based on the Rihaczek Distribution is compared with the parametric estimator based on the high-order ambiguity function for their accuracy in estimating phase synchrony.
Louis L. Scharf - One of the best experts on this subject based on the ideXlab platform.
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a geometric interpretation of the Rihaczek time frequency Distribution for stochastic signals
International Symposium on Information Theory, 2005Co-Authors: Peter J. Schreier, Louis L. Scharf, Alfred HanssenAbstract:Based on the Cramer-Loeve spectral representation for a harmonizable random process, the Rihaczek Distribution is a time- and frequency-shift covariant, bilinear time-frequency Distribution. It can be expressed as a complex Hilbert space inner product between the time series and its infinitesimal stochastic Fourier generator. We show that we may attach an illuminating geometry to this inner product, wherein the cosine-squared of the angle between the time series and its infinitesimal stochastic Fourier generator is given by the Rihaczek Distribution. We propose to construct estimators of the Rihaczek Distribution using a factored kernel in Cohen's class of bilinear time-frequency Distributions
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The Hilbert space geometry of the Rihaczek Distribution for stochastic analytic signals
IEEE Signal Processing Letters, 2005Co-Authors: Louis L. Scharf, Peter J. Schreier, Alfred HanssenAbstract:The Rihaczek Distribution for stochastic signals is a time- and frequency-shift covariant bilinear time-frequency Distribution (TFD) based on the Crame/spl acute/r-Loe/spl grave/ve spectral representation for a harmonizable process. It is a complex Hilbert space inner product (or cross correlation) between the time series and its infinitesimal stochastic Fourier generator. To this inner product, we may attach an illuminating geometry, wherein the cosine squared of the angle between the time series and its infinitesimal stochastic Fourier generator is given by the Rihaczek Distribution. The Rihaczek Distribution also determines a time-varying Wiener filter for estimating a time series from its infinitesimal stochastic Fourier generator and measures the resulting error covariance. We propose a factored kernel to construct estimators of the Rihaczek Distribution that are contained in Cohen's class of bilinear TFDs.
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ISIT - A geometric interpretation of the Rihaczek time-frequency Distribution for stochastic signals
Proceedings. International Symposium on Information Theory 2005. ISIT 2005., 2005Co-Authors: Peter J. Schreier, Louis L. Scharf, Alfred HanssenAbstract:Based on the Cramer-Loeve spectral representation for a harmonizable random process, the Rihaczek Distribution is a time- and frequency-shift covariant, bilinear time-frequency Distribution. It can be expressed as a complex Hilbert space inner product between the time series and its infinitesimal stochastic Fourier generator. We show that we may attach an illuminating geometry to this inner product, wherein the cosine-squared of the angle between the time series and its infinitesimal stochastic Fourier generator is given by the Rihaczek Distribution. We propose to construct estimators of the Rihaczek Distribution using a factored kernel in Cohen's class of bilinear time-frequency Distributions
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EUSIPCO - Complex time-frequency and dual-frequency spectra of harmonizable processes
2004Co-Authors: Alfred Hanssen, Y. Larsen, Louis L. ScharfAbstract:Harmonizable processes form a huge and useful class of nonstationary random processes. In this paper, we will discuss the properties of, and some consequences of employing a natural choice of complex valued densities to characterize the harmonizable class. In particular, we will discuss the Hilbert space geometry of the resulting complex time-frequency description (related to the Rihaczek Distribution), and the dual-frequency description (related to the Loeve spectrum). We will demonstrate that useful normalized nonstationary generalizations of coherence emerge from this picture. Finally, we extend the formalism to random fields and to higher-order
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The Hilbert space geometry of the stochastic Rihaczek Distribution
Conference Record of Thirty-Fifth Asilomar Conference on Signals Systems and Computers (Cat.No.01CH37256), 2001Co-Authors: Louis L. Scharf, Benjamin Friedlander, P. Flandrin, Alfred HanssenAbstract:Beginning with the Cramer-Loeve spectral representation for a nonstationary discrete-time random process, one may derive the stochastic Rihaczek Distribution as a natural time-frequency Distribution. This Distribution is within one Fourier transform of the time-varying correlation and the frequency-varying correlogram, and within two of the ambiguity function. But, more importantly, it is a complex Hilbert space inner product, or cross-correlation, between the time series and its one-term Fourier expansion. To this inner product we may attach an illuminating geometry. Moreover, the Rihaczek Distribution determines a time-varying Wiener filter for estimating the time series from its local spectrum, the error covariance of the estimator, and the related time-varying coherence. The squared coherence is the magnitude-squared of the complex Rihaczek Distribution, normalized by its time and frequency marginals. It is this squared coherence that determines the time-varying localization of the time series in frequency. Most of these insights extend to the characterization of time-varying and random channels, in which case the stochastic Rihaczek Distribution is a fine-grained characterization of the channel that complements the coarse-grained characterization given by the ambiguity function.
Ali Yener Mutlu - One of the best experts on this subject based on the ideXlab platform.
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A Time-Frequency-Based Approach to Phase and Phase Synchrony Estimation
IEEE Transactions on Signal Processing, 2011Co-Authors: Selin Aviyente, Ali Yener MutluAbstract:Time-varying phase synchrony is an important bivariate measure that quantifies the dynamics between nonstationary signals and has been widely used in many applications including chaotic oscillators in physics and multichannel electroencephalography recordings in neuroscience. Current state-of-the-art in time-varying phase estimation uses either the Hilbert transform or the complex wavelet transform of the signals. Both of these methods have some major drawbacks such as the assumption that the signals are narrowband for the Hilbert transform and the nonuniform time-frequency resolution inherent to the wavelet analysis. In this paper, a new phase estimation method based on the Rihaczek Distribution and Reduced Interference Rihaczek Distribution belonging to Cohen's class is proposed. These Distributions offer phase estimates with uniformly high time-frequency resolution which can be used for defining time and frequency dependent phase synchrony. Properties of the phase estimator and the corresponding phase synchrony measure are evaluated both analytically and through simulations showing the effectiveness of the new measures compared to existing methods.
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Comparison of nonparametric and parametric time-varying methods for quantifying phase synchrony
2010 Conference Record of the Forty Fourth Asilomar Conference on Signals Systems and Computers, 2010Co-Authors: Ali Yener Mutlu, Selin AviyenteAbstract:Quantifying the pairwise relationships between two signals is an important problem in many fields of science and engineering. Phase synchrony has been suggested as a powerful tool for determining bivariate signal relationships. Recently, a nonparametric phase estimation method based on the Rihaczek Distribution belonging to Cohen's class of time-frequency Distributions (TFDs) has been proposed for the estimation of time-varying phase [1]. Alternatively, parametric time-frequency methods, which model the phase as a polynomial, can be used. In this paper, the nonparametric phase estimator based on the Rihaczek Distribution is compared with the parametric estimator based on the high-order ambiguity function for their accuracy in estimating phase synchrony.
Peter J. Schreier - One of the best experts on this subject based on the ideXlab platform.
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a geometric interpretation of the Rihaczek time frequency Distribution for stochastic signals
International Symposium on Information Theory, 2005Co-Authors: Peter J. Schreier, Louis L. Scharf, Alfred HanssenAbstract:Based on the Cramer-Loeve spectral representation for a harmonizable random process, the Rihaczek Distribution is a time- and frequency-shift covariant, bilinear time-frequency Distribution. It can be expressed as a complex Hilbert space inner product between the time series and its infinitesimal stochastic Fourier generator. We show that we may attach an illuminating geometry to this inner product, wherein the cosine-squared of the angle between the time series and its infinitesimal stochastic Fourier generator is given by the Rihaczek Distribution. We propose to construct estimators of the Rihaczek Distribution using a factored kernel in Cohen's class of bilinear time-frequency Distributions
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The Hilbert space geometry of the Rihaczek Distribution for stochastic analytic signals
IEEE Signal Processing Letters, 2005Co-Authors: Louis L. Scharf, Peter J. Schreier, Alfred HanssenAbstract:The Rihaczek Distribution for stochastic signals is a time- and frequency-shift covariant bilinear time-frequency Distribution (TFD) based on the Crame/spl acute/r-Loe/spl grave/ve spectral representation for a harmonizable process. It is a complex Hilbert space inner product (or cross correlation) between the time series and its infinitesimal stochastic Fourier generator. To this inner product, we may attach an illuminating geometry, wherein the cosine squared of the angle between the time series and its infinitesimal stochastic Fourier generator is given by the Rihaczek Distribution. The Rihaczek Distribution also determines a time-varying Wiener filter for estimating a time series from its infinitesimal stochastic Fourier generator and measures the resulting error covariance. We propose a factored kernel to construct estimators of the Rihaczek Distribution that are contained in Cohen's class of bilinear TFDs.
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ISIT - A geometric interpretation of the Rihaczek time-frequency Distribution for stochastic signals
Proceedings. International Symposium on Information Theory 2005. ISIT 2005., 2005Co-Authors: Peter J. Schreier, Louis L. Scharf, Alfred HanssenAbstract:Based on the Cramer-Loeve spectral representation for a harmonizable random process, the Rihaczek Distribution is a time- and frequency-shift covariant, bilinear time-frequency Distribution. It can be expressed as a complex Hilbert space inner product between the time series and its infinitesimal stochastic Fourier generator. We show that we may attach an illuminating geometry to this inner product, wherein the cosine-squared of the angle between the time series and its infinitesimal stochastic Fourier generator is given by the Rihaczek Distribution. We propose to construct estimators of the Rihaczek Distribution using a factored kernel in Cohen's class of bilinear time-frequency Distributions
