A suboptimal estimator of the sampling jitter variance using the bispectrum

Ilan Sharfer, Hagit Messer

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the problem of estimating parameters of an irregular sampling process defined as a uniform sampling process in which the deviations from the nominal sampling times constitute a random IID process (jitter). Emphasis is placed on estimating the variance of the jitter, based on observation of samples taken from a continuous band-limited third-order stationary process. We derive an estimation procedure which uses the bispectrum estimates of a process with a priori known bispectrum. Derivation of the generalized likelihood ratio in the bispectral domain, leads to a statistic with which a bispectrum-based maximum likelihood estimation can be done. We propose a suboptimal estimator, and show that it is asymptotically unbiased and consistent. The dependence of the estimator's performance on the data length and the skewness is studied for a specific example. The estimator's variance is compared to the bispectrum-based Cramer-Rao bound (BCRB), and is shown to approach it for sufficiently large data length or skewness. Computer simulations verify the effectiveness of the proposed estimation method for small jitter.

Original languageEnglish
Pages (from-to)169-186
Number of pages18
JournalSignal Processing
Volume38
Issue number2
DOIs
StatePublished - Jul 1994

Keywords

  • Bispectrum
  • Higher order spectra
  • Jitter
  • Sampling noise

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