Fractional sampling theorem for -bandlimited random signals and its relation to the von neumann ergodic theorem
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Date
2014
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Institute of Electrical and Electronics Engineers Inc.
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.
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IEEE Transactions on Signal Processing; Vol. 62, Núm. 14; pp. 3695-3705