The Experts below are selected from a list of 252 Experts worldwide ranked by ideXlab platform
L. Stankovic - One of the best experts on this subject based on the ideXlab platform.
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Wigner Distribution reconstruction from two projections
Proceedings of the 11th IEEE Signal Processing Workshop on Statistical Signal Processing (Cat. No.01TH8563), 2001Co-Authors: T. Alieva, M.j. Bastiaans, L. StankovicAbstract:The connection between the instantaneous frequency and the angle derivative of the fractional power spectra is established. It permits to solve the signal retrieval problem if only two close fractional power spectra are known. This fact is used in the reconstruction of the Wigner Distribution or the pseudo Wigner Distribution from two close projections.
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Fractional-Fourier-domain weighted Wigner Distribution
Proceedings of the 11th IEEE Signal Processing Workshop on Statistical Signal Processing (Cat. No.01TH8563), 2001Co-Authors: L. Stankovic, T. Alieva, M.j. BastiaansAbstract:A fractional-Fourier-domain realization of the weighted Wigner Distribution (or S-method), producing auto-terms close to the ones in the Wigner Distribution itself, but with reduced cross-terms, is presented. The computational cost of this fractional-domain realization is the same as the computational cost of the realizations in the time or the frequency domain, since the short-time Fourier transform of the fractional Fourier transform of a signal corresponds to the short-time Fourier transform of the signal itself, with the window being the fractional Fourier transform of the initial one. The appropriate fractional domain is found from the analysis of the second-order fractional Fourier transform moments. Numerical simulations show a qualitative advantage in the time-frequency representation, when the calculation is done in the optimal fractional domain.
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The robust Wigner Distribution
2000 IEEE International Conference on Acoustics Speech and Signal Processing. Proceedings (Cat. No.00CH37100), 2000Co-Authors: L. Stankovic, I. Djurovic, S. StankovicAbstract:The standard short-time Fourier transform and the Wigner Distribution can be obtained as solutions of the minimization problem, with the absolute square error as a loss function. It has been shown that some other loss functions, like for example the absolute error, can produce more robust results in the case of signals corrupted with impulse, heavy-tailed, noise. This paper presents robust time frequency-signal analysis of nonstationary signals, corrupted with heavy-tailed noise. For this purpose the robust Wigner Distribution is introduced, as an extension of the robust M-periodogram concept. The theory is illustrated on several examples, including application of the proposed Distribution on the instantaneous frequency estimation.
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a method for improved Distribution concentration in the time frequency analysis of multicomponent signals using the l Wigner Distribution
IEEE Transactions on Signal Processing, 1995Co-Authors: L. StankovicAbstract:The energy location in the Cohen class of time-frequency Distributions is analyzed. If the instantaneous frequency is linear, then only the Wigner Distribution produces the ideal energy concentration. The scaled version of the Wigner Distribution (L-Wigner Distribution), is used to improve the time-frequency representation of signals with nonlinear instantaneous frequencies. In the case of multicomponent signals, the cross terms, appearing in the Wigner Distribution and in the L-Wigner Distribution, can be easily removed or reduced in a computationally very efficient way. The theory is illustrated on the numerical examples with multicomponent noisy signals. >
Eugenia Malinnikova - One of the best experts on this subject based on the ideXlab platform.
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zeros of the Wigner Distribution and the short time fourier transform
Revista Matematica Complutense, 2019Co-Authors: Karlheinz Grochenig, Philippe Jaming, Eugenia MalinnikovaAbstract:We study the question under which conditions the zero set of a (cross-) Wigner Distribution W(f, g) or a short-time Fourier transform is empty. This is the case when both f and g are generalized Gaussians, but we will construct less obvious examples consisting of exponential functions and their convolutions. The results require elements from the theory of totally positive functions, Bessel functions, and Hurwitz polynomials. The question of zero-free Wigner Distributions is also related to Hudson’s theorem for the positivity of the Wigner Distribution and to Hardy’s uncertainty principle. We then construct a class of step functions S so that the Wigner Distribution $$W(f,\mathbf {1}_{(0,1)})$$ always possesses a zero $$f\in S \cap L^p$$ when $$p<\infty $$, but may be zero-free for $$f\in S \cap L^\infty $$. The examples show that the question of zeros of the Wigner Distribution may be quite subtle and relate to several branches of analysis.
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Zeros of the Wigner Distribution and the short-time Fourier transform
Revista Matemática Complutense, 2019Co-Authors: Karlheinz Grochenig, Philippe Jaming, Eugenia MalinnikovaAbstract:We study the question under which conditions the zero set of a (cross-) Wigner Distribution W ( f , g ) or a short-time Fourier transform is empty. This is the case when both f and g are generalized Gaussians, but we will construct less obvious examples consisting of exponential functions and their convolutions. The results require elements from the theory of totally positive functions, Bessel functions, and Hurwitz polynomials. The question of zero-free Wigner Distributions is also related to Hudson’s theorem for the positivity of the Wigner Distribution and to Hardy’s uncertainty principle. We then construct a class of step functions S so that the Wigner Distribution $$W(f,\mathbf {1}_{(0,1)})$$ W ( f , 1 ( 0 , 1 ) ) always possesses a zero $$f\in S \cap L^p$$ f ∈ S ∩ L p when $$p
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zeros of the Wigner Distribution and the short time fourier transform
arXiv: Classical Analysis and ODEs, 2018Co-Authors: Karlheinz Grochenig, Philippe Jaming, Eugenia MalinnikovaAbstract:We study the question under which conditions the zero set of a (cross-) Wigner Distribution W (f, g) or a short-time Fourier transform is empty. This is the case when both f and g are generalized Gaussians, but we will construct less obvious examples consisting of exponential functions and their convolutions. The results require elements from the theory of totally positive functions, Bessel functions, and Hurwitz polynomials. The question of zero-free Wigner Distributions is also related to Hudson's theorem for the positivity of the Wigner Distribution and to Hardy's uncertainty principle. We then construct a class of step functions S so that the Wigner Distribution W (f, 1 (0,1)) always possesses a zero f $\in$ S $\cap$ L p for p < $\infty$, but may be zero-free for f $\in$ S $\cap$ L $\infty$. The examples show that the question of zeros of the Wigner Distribution may be quite subtle and relate to several branches of analysis.
Patrik Wahlberg - One of the best experts on this subject based on the ideXlab platform.
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The Wigner Distribution of Gaussian weakly harmonizable sprocesses
2020Co-Authors: Patrik WahlbergAbstract:The paper treats the Wigner Distribution of scalar-valued stochastic processes defined on R-d. We show that if the process is Gaussian and weakly harmonizable then a stochastic Wigner Distribution is well defined. The special cas, of stationary processes is studied, in which case the Wigner Distribution is weakly stationary in the time variable and the variance is equal to the deterministic Wigner Distribution of the covariance function.
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The Wigner Distribution of Gaussian Weakly Harmonizable Stochastic Processes
Pseudo-Differential Operators and Related Topics, 2020Co-Authors: Patrik WahlbergAbstract:The paper treats the Wigner Distribution of scalar-valued stochastic processes defined on ℝd. We show that if the process is Gaussian and weakly harmonizable then a stochastic Wigner Distribution is well defined. The special case of stationary processes is studied, in which case the Wigner Distribution is weakly stationary in the time variable and the variance is equal to the deterministic Wigner Distribution of the covariance function.
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The Wave Front Set of the Wigner Distribution and Instantaneous Frequency
Journal of Fourier Analysis and Applications, 2011Co-Authors: Paolo Boggiatto, Alessandro Oliaro, Patrik WahlbergAbstract:We prove a formula expressing the gradient of the phase function of a function f:ℝ d ↦ℂ as a normalized first frequency moment of the Wigner Distribution for fixed time. The formula holds when f is the Fourier transform of a Distribution of compact support, or when f belongs to a Sobolev space H d/2+1+e (ℝ d ) where e>0. The restriction of the Wigner Distribution to fixed time is well defined provided a certain condition on its wave front set is satisfied. Therefore we first need to study the wave front set of the Wigner Distribution of a tempered Distribution.
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The wave front set of the Wigner Distribution and instantaneous frequency
arXiv: Functional Analysis, 2010Co-Authors: Paolo Boggiatto, Alessandro Oliaro, Patrik WahlbergAbstract:We prove a formula expressing the gradient of the phase function of a function $f: \mathbb R^d \mapsto \mathbb C$ as a normalized first frequency moment of the Wigner Distribution for fixed time. The formula holds when $f$ is the Fourier transform of a Distribution of compact support, or when $f$ belongs to a Sobolev space $H^{d/2+1+\epsilon}(\mathbb R^d)$ where $\epsilon>0$. The restriction of the Wigner Distribution to fixed time is well defined provided a certain condition on its wave front set is satisfied. Therefore we first study the wave front set of the Wigner Distribution of a tempered Distribution.
S. Stankovic - One of the best experts on this subject based on the ideXlab platform.
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Local frequency estimation based on the Wigner Distribution
Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205), 2001Co-Authors: I. Djurovic, S. Stankovic, L.a. Stankovic, R. StojanovicAbstract:The asymptotic performance of the local frequency (LF) estimator, based on the Wigner Distribution (WD) of multidimensional signals, is considered. The optimal estimation window size, producing minimal mean squared error (MSE), is derived. The results are illustrated and confirmed by numerical examples.
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The robust Wigner Distribution
2000 IEEE International Conference on Acoustics Speech and Signal Processing. Proceedings (Cat. No.00CH37100), 2000Co-Authors: L. Stankovic, I. Djurovic, S. StankovicAbstract:The standard short-time Fourier transform and the Wigner Distribution can be obtained as solutions of the minimization problem, with the absolute square error as a loss function. It has been shown that some other loss functions, like for example the absolute error, can produce more robust results in the case of signals corrupted with impulse, heavy-tailed, noise. This paper presents robust time frequency-signal analysis of nonstationary signals, corrupted with heavy-tailed noise. For this purpose the robust Wigner Distribution is introduced, as an extension of the robust M-periodogram concept. The theory is illustrated on several examples, including application of the proposed Distribution on the instantaneous frequency estimation.
T. Stouraitis - One of the best experts on this subject based on the ideXlab platform.
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VLSI architectures for the implementation of the Wigner Distribution
2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353), 2002Co-Authors: D. Zografos, K. Karagianni, T. StouraitisAbstract:The Wigner Distribution is a valuable tool for time-frequency signal analysis. Two different VLSI architectures for the real-time implementation of the Wigner Distribution algorithm are proposed in this paper, with the objective of pointing out various computational issues that are involved. Reduction of the computational load of the algorithm, as well as reduction of the memory requirements has been achieved mostly by applying simple trigonometric properties to the original expression of the algorithm. The addressing schemes to access the memory blocks are also proposed.