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

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.

• Fecha de publicación: 2013
• Institución: Universidad Tecnológica de Bolívar
• Repositorio: Repositorio Institucional UTB
• Idioma: eng
• OAI Identifier: oai:repositorio.utb.edu.co:20.500.12585/9077
• Acceso en línea: https://hdl.handle.net/20.500.12585/9077
• Palabra clave: 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
• Rights: restrictedAccess
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/