Alias-Free Spectral Estimation of Stochastic Processes

Electrical Engineering;Applied Mathematics

Adegbola, Mashood Olayide ; Martel, Hardy Cross (advisor)

University:California Institute of Technology

Department:Engineering and Applied Science

关键词: Electrical Engineering;    Applied Mathematics;   

Others  :  https://thesis.library.caltech.edu/10504/1/Adegbola_mo_1971.pdf

美国|英语

来源: Caltech THESIS

【 摘 要 】

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.