Alias-Free Spectral Estimation of Stochastic Processes

Citation

Adegbola, Mashood Olayide (1971) Alias-Free Spectral Estimation of Stochastic Processes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ymat-1n64. https://resolver.caltech.edu/CaltechTHESIS:10112017-132121017

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 {t_n} is assumed to be stationary point process statistically independent of the sampled process X(t). Stationarity of {t_n} admits that joint statistics of t_k, t_k+n do not depend on k. Closed form analytical formulae are derived for the spectral window Q_m(f) and for cov{S^{^}(f_r), S^{^}(f_q)}, var{S^{^}(f_r)} 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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