Fractional sampling theorem for -bandlimited random signals and its relation to the von neumann ergodic theorem

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.

• Fecha de publicación: 2014
• Institución: Universidad Tecnológica de Bolívar
• Repositorio: Repositorio Institucional UTB
• Idioma: eng
• OAI Identifier: oai:repositorio.utb.edu.co:20.500.12585/9036
• Acceso en línea: https://hdl.handle.net/20.500.12585/9036
• Palabra clave: Fractional correlation; Fractional power spectrum; Ractional Fourier transform; Sampling theorem; Stochastic processes; Power spectral density; Random processes; Fractional correlation; Fractional Fourier transforms; Fractional power; Fractional power spectral density; Fractional sampling; Interpolation formulas; Sampling theorems; Stationary random signal; Digital signal processing
• Rights: restrictedAccess
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/