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

Abstract

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.