Frequency estimation from crossings of an unknown level

Cuzick Jack, Georg Lindgren

Research output: Contribution to journalArticlepeer-review


By counting the number of upcrossings of the mean level by a stationary Gaussian process one can estimate the mean frequency of the process. Here we present a frequency estimator based on the number of upcrossings of one unknown level hoped to be near the mean, and the percentage of the total observation time spent above the level. This is equivalent to observing upcrossings of a known level in a process with unknown mean and variance. Formulae are given for the bias and variance of the estimator, and conditions for its asymptotic normality. Numerical examples show that the estimator behaves reasonably for levels within one standard deviation from the process mean.
Original languageEnglish
Pages (from-to)65-72
Issue number1
Publication statusPublished - 1980

Subject classification (UKÄ)

  • Probability Theory and Statistics

Free keywords

  • Central limit theorem
  • Gaussian process
  • Level crossing
  • Mean frequency
  • Spectral moment


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