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Alias-Free Spectral Estimation of Stochastic Processes


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


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Electrical Engineering and Applied Mathematics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Electrical Engineering
Minor Option:Applied Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Martel, Hardy Cross (advisor)
  • Caughey, Thomas Kirk (advisor)
Thesis Committee:
  • Caughey, Thomas Kirk (chair)
  • George, Nicholas A.
  • Martel, Hardy Cross
  • Todd, John
  • Whitham, Gerald Beresford
Defense Date:15 April 1971
Funding AgencyGrant Number
Record Number:CaltechTHESIS:10112017-132121017
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10504
Deposited By: Benjamin Perez
Deposited On:11 Oct 2017 21:01
Last Modified:29 May 2024 21:50

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