Browsing by Author "Torres R."
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Item An a posteriori error estimator for a non-conforming domain decomposition method for a harmonic elastodynamics equation(Global Science Press, 2018) Domínguez C.; Torres R.; González H.We develop a reliable residual-based a posteriori error estimator for a nonconforming method with non-matching meshes for a harmonic elastodynamics equation and show that the approximation method converges with an optimal order to the exact solution. Moreover, we propose an adaptive strategy to reduce computational cost and derive better approximations for problems with singularities and with large approximating systems. Numerical experiments confirm theoretical conclusions. © 2018 Global-Science Press.Item Diffuser in Fractional Fourier Optics(OSA - The Optical Society, 2016) Patiño Vanegas, Alberto; Durand, P.E.; Pellat-Finet P.; Torres R.We propose a method for calculating a bandlimited diffuser with smooth spectrum in the Fresnel domain without any 2p phase ambiguities using the fractional Fourier transform. Such diffusers are necessary to avoid problems of speckles. © OSA 2016.Item Fractional Fourier analysis of random signals and the notion of α -Stationarity of the Wigner-Ville distribution(2013) Torres R.; Torres E.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=pi2, and it leads to the Wiener-Khinchin theorem. © 1991-2012 IEEE.Item Fractional sampling theorem for -bandlimited random signals and its relation to the von neumann ergodic theorem(Institute of Electrical and Electronics Engineers Inc., 2014) Torres R.; Lizarazo Z.; Torres E.Considering that fractional correlation function and the fractional power spectral density, for -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 -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. © 2014 IEEE.Item α-bandlimited diffuser in fractional Fourier optics(SPIE, 2016) Patiño Vanegas, Alberto; Durand, P.E.; Torres R.; Pellat-Finet P.; Sheridan J.T.; Meuret Y.; Wyrowski F.We propose a method for calculating appropriate α-band limited diffusers using the fractional Fourier transform. In order to do this, we implement a method for performing a numerical interpolation in the fractional Fourier domain. Such diffusers with compact support in the Fresnel regime may be used in fractional Fourier optical systems where the use of diffusers produce speckles, e.g. digital holography or optical encryption. Numerical simulations are presented. © 2016 SPIE.