2020-03-262020-03-262013IEEE Transactions on Signal Processing; Vol. 61, Núm. 6; pp. 1555-15601053587Xhttps://hdl.handle.net/20.500.12585/9077In 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 electrónicoapplication/pdfenghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/article10.1109/TSP.2012.2236834Fractional correlationFractional Fourier transformationFractional power spectral densityRandom signalsWiener-Khinchin theoremWigner-Ville distributionFractional correlationFractional Fourier TransformationsFractional power spectral densityRandom signalWiener-Khinchin theoremFourier opticsPower spectral densityWigner-Ville distributionFourier analysisinfo:eu-repo/semantics/restrictedAccessAtribución-NoComercial 4.0 InternacionalUniversidad Tecnológica de BolívarRepositorio UTB5627089690035094573000