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Torres R. Torres E. 2020-03-26T16:32:54Z 2020-03-26T16:32:54Z 2013 IEEE Transactions on Signal Processing; Vol. 61, Núm. 6; pp. 1555-1560 1053587X https://hdl.handle.net/20.500.12585/9077 10.1109/TSP.2012.2236834 Universidad Tecnológica de Bolívar Repositorio UTB 56270896900 35094573000 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. Recurso electrónico application/pdf eng http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/restrictedAccess Atribución-NoComercial 4.0 Internacional https://www.scopus.com/inward/record.uri?eid=2-s2.0-84875015943&doi=10.1109%2fTSP.2012.2236834&partnerID=40&md5=8948c99af3dc2f6f9bcba86bcaee6a4d Fractional Fourier analysis of random signals and the notion of α -Stationarity of the Wigner-Ville distribution Artículo info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Fractional correlation Fractional Fourier transformation Fractional power spectral density Random signals Wiener-Khinchin theorem Wigner-Ville distribution Fractional correlation Fractional Fourier Transformations Fractional power spectral density Random signal Wiener-Khinchin theorem Fourier optics Power spectral density Wigner-Ville distribution Fourier analysis Namias, V., The fractional order Fourier transform and its application to quantum mechanics (1980) J. Inst. Math. 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