The Experts below are selected from a list of 54 Experts worldwide ranked by ideXlab platform
Edmanuel Torres - One of the best experts on this subject based on the ideXlab platform.
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Fractional Sampling Theorem for $\alpha$-Bandlimited Random Signals and Its Relation to the von Neumann Ergodic Theorem
IEEE Transactions on Signal Processing, 2014Co-Authors: Rafael Torres, Zandra Lizarazo, Edmanuel TorresAbstract:Considering that fractional correlation function and the fractional power spectral density, for α-stationary random signals, form a fractional Fourier Transform Pair. We present an interpolation formula to estimate a random signal from a temporal random series, based on the fractional sampling theorem for α-bandlimited random signals. Furthermore, by establishing the relationship between the sampling theorem and the von Neumann ergodic theorem, the estimation of the power spectral density of a random signal from one sample signal becomes a suitable approach. Thus, the validity of the sampling theorem for random signals is closely linked to an ergodic hypothesis in the mean sense.
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fractional Fourier analysis of random signals and the notion of spl alpha stationarity of the wigner ville distribution
IEEE Transactions on Signal Processing, 2013Co-Authors: Rafael Torres, Edmanuel TorresAbstract:In this paper, a generalized notion of wide-sense α-stationarity for random signals is presented. The notion of stationarity is fundamental in the Fourier analysis of random signals. For this purpose, a definition of the fractional correlation between two random variables is introduced. It is shown that for wide-sense α -stationary random signals, the fractional correlation and the fractional power spectral density functions form a fractional Fourier Transform Pair. Thus, the concept of α -stationarity plays an important role in the analysis of random signals through the fractional Fourier Transform for signals nonstationary in the standard formulation, but α -stationary. Furthermore, we define the α-Wigner-Ville distribution in terms of the fractional correlation function, in which the standard Fourier analysis is the particular case for α = π/2 , and it leads to the Wiener-Khinchin theorem.
Rafael Torres - One of the best experts on this subject based on the ideXlab platform.
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Fractional Sampling Theorem for $\alpha$-Bandlimited Random Signals and Its Relation to the von Neumann Ergodic Theorem
IEEE Transactions on Signal Processing, 2014Co-Authors: Rafael Torres, Zandra Lizarazo, Edmanuel TorresAbstract:Considering that fractional correlation function and the fractional power spectral density, for α-stationary random signals, form a fractional Fourier Transform Pair. We present an interpolation formula to estimate a random signal from a temporal random series, based on the fractional sampling theorem for α-bandlimited random signals. Furthermore, by establishing the relationship between the sampling theorem and the von Neumann ergodic theorem, the estimation of the power spectral density of a random signal from one sample signal becomes a suitable approach. Thus, the validity of the sampling theorem for random signals is closely linked to an ergodic hypothesis in the mean sense.
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fractional Fourier analysis of random signals and the notion of spl alpha stationarity of the wigner ville distribution
IEEE Transactions on Signal Processing, 2013Co-Authors: Rafael Torres, Edmanuel TorresAbstract:In this paper, a generalized notion of wide-sense α-stationarity for random signals is presented. The notion of stationarity is fundamental in the Fourier analysis of random signals. For this purpose, a definition of the fractional correlation between two random variables is introduced. It is shown that for wide-sense α -stationary random signals, the fractional correlation and the fractional power spectral density functions form a fractional Fourier Transform Pair. Thus, the concept of α -stationarity plays an important role in the analysis of random signals through the fractional Fourier Transform for signals nonstationary in the standard formulation, but α -stationary. Furthermore, we define the α-Wigner-Ville distribution in terms of the fractional correlation function, in which the standard Fourier analysis is the particular case for α = π/2 , and it leads to the Wiener-Khinchin theorem.
Djurdje Cvijovic - One of the best experts on this subject based on the ideXlab platform.
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another discrete Fourier Transform Pairs associated with the lipschitz lerch zeta function
Applied Mathematics and Computation, 2012Co-Authors: Djurdje CvijovicAbstract:Abstract It is demonstrated that the alternating Lipschitz–Lerch zeta function and the alternating Hurwitz zeta function constitute a discrete Fourier Transform Pair. This discrete Transform Pair makes it possible to deduce, as special cases and consequences, many (mainly new) Transformation relations involving the values at rational arguments of alternating variants of various zeta functions, such as the Lerch and Hurwitz zeta functions and Legendre chi function.
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some discrete Fourier Transform Pairs associated with the lipschitz lerch zeta function
Applied Mathematics Letters, 2009Co-Authors: Djurdje Cvijovic, H M SrivastavaAbstract:Abstract It is shown that there exists a companion formula to Srivastava’s formula for the Lipschitz–Lerch Zeta function [see H.M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc. 129 (2000) 77–84] and that together these two results form a discrete Fourier Transform Pair. This Fourier Transform Pair makes it possible for other (known or new) results involving the values of various Zeta functions at rational arguments to be easily recovered or deduced in a more general context and in a remarkably unified manner.
Zandra Lizarazo - One of the best experts on this subject based on the ideXlab platform.
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Fractional Sampling Theorem for $\alpha$-Bandlimited Random Signals and Its Relation to the von Neumann Ergodic Theorem
IEEE Transactions on Signal Processing, 2014Co-Authors: Rafael Torres, Zandra Lizarazo, Edmanuel TorresAbstract:Considering that fractional correlation function and the fractional power spectral density, for α-stationary random signals, form a fractional Fourier Transform Pair. We present an interpolation formula to estimate a random signal from a temporal random series, based on the fractional sampling theorem for α-bandlimited random signals. Furthermore, by establishing the relationship between the sampling theorem and the von Neumann ergodic theorem, the estimation of the power spectral density of a random signal from one sample signal becomes a suitable approach. Thus, the validity of the sampling theorem for random signals is closely linked to an ergodic hypothesis in the mean sense.
H M Srivastava - One of the best experts on this subject based on the ideXlab platform.
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some discrete Fourier Transform Pairs associated with the lipschitz lerch zeta function
Applied Mathematics Letters, 2009Co-Authors: Djurdje Cvijovic, H M SrivastavaAbstract:Abstract It is shown that there exists a companion formula to Srivastava’s formula for the Lipschitz–Lerch Zeta function [see H.M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc. 129 (2000) 77–84] and that together these two results form a discrete Fourier Transform Pair. This Fourier Transform Pair makes it possible for other (known or new) results involving the values of various Zeta functions at rational arguments to be easily recovered or deduced in a more general context and in a remarkably unified manner.