Alias-Free Spectral Estimation of Stochastic Processes

Author: Adegbola, Mashood Olayide

Year: 1971

Degree: Dissertation (Ph.D.)

Advisors: Martel, Hardy Cross; Caughey, Thomas Kirk

Committee Members: Caughey, Thomas Kirk; George, Nicholas A.; Martel, Hardy Cross; Todd, John; Whitham, Gerald Beresford

Option: Electrical Engineering; Applied Mathematics

DOI: 10.7907/ymat-1n64

Abstract

A scheme for the practical estimation of power spectrum from randomly-timed samples is proposed and investigated for wide-sense stationary point processes. The sampling process {tn} is assumed to be stationary point process statistically independent of the sampled process X(t). Stationarity of {tn} admits that joint statistics of tk, tk+n do not depend on k. Closed form analytical formulae are derived for the spectral window Qm(f) and for cov{S^(fr), S^(fq)}, var{S^(fr)} for the particular case of independent identically distributed sampling intervals. Results confirm the alias-free character of the Poisson sampling scheme even for non-bandlimited spectra. It is shown further that for Gaussian processes with very smooth spectra Poisson sampling process can yield more reliable estimates (i.e., with a smaller variance) than the well known method of periodic sampling.

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