Fractional Fourier analysis of random signals and the notion of α -Stationarity of the Wigner-Ville distribution

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DOIResolve DOI: http://doi.org/10.1109/TSP.2012.2236834
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TypeArticle
Journal titleIEEE Transactions on Signal Processing
ISSN1053-587X
Volume61
Issue6
Article number6397633
Pages15551560; # of pages: 6
SubjectFractional correlation; Fractional Fourier Transformations; Fractional power spectral density; Random signal; Wiener-Khinchin theorem; Fourier optics; Power spectral density; Wigner-Ville distribution; Fourier analysis
AbstractIn 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.
Publication date
LanguageEnglish
AffiliationNational Research Council Canada (NRC-CNRC); Security and Disruptive Technologies
Peer reviewedYes
NPARC number21271800
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Record identifier0772a7f6-a773-45be-8be6-204a0413cce4
Record created2014-04-22
Record modified2016-05-09
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