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Frequency estimation from crossings of an observed mean level

Åke, Björnham and Lindgren, Georg LU (1976) In Biometrika 63(3). p.507-512
Abstract
By counting the number of upcrossings of the mean level by a stationary Gaussian process one can estimate the mean frequency of the process. If the mean level is unknown and estimated from the observed mean level, then this crossing estimator is more or less biased, depending on the length of the observation interval. It is shown that if the interval is at least two mean wavelengths, then the bias is small and of the same order as the standard deviation of a certain unbiased zero crossing estimator. Therefore the crossing method gives a simple and reliable technique for automatic estimation of the mean frequenoy of a process over long periods of time, which may involve changes in the mean level and covariance function.
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Estimation of the mean, Level crossings, Mean frequency, Spectral moment, Stationary normal process, Time series estimation
in
Biometrika
volume
63
issue
3
pages
507 - 512
publisher
Biometrika Trust
external identifiers
  • Scopus:0017109038
ISSN
0006-3444
DOI
10.1093/biomet/63.3.507
language
English
LU publication?
no
id
bdcf7b4f-fd13-40e9-9dc0-601b91cbcc37 (old id 1273150)
alternative location
http://ida.lub.lu.se/cgi-bin/oup_local/biomet/63_3/63-3-507.pdf
date added to LUP
2009-06-02 16:23:17
date last changed
2016-10-13 04:35:50
@misc{bdcf7b4f-fd13-40e9-9dc0-601b91cbcc37,
  abstract     = {By counting the number of upcrossings of the mean level by a stationary Gaussian process one can estimate the mean frequency of the process. If the mean level is unknown and estimated from the observed mean level, then this crossing estimator is more or less biased, depending on the length of the observation interval. It is shown that if the interval is at least two mean wavelengths, then the bias is small and of the same order as the standard deviation of a certain unbiased zero crossing estimator. Therefore the crossing method gives a simple and reliable technique for automatic estimation of the mean frequenoy of a process over long periods of time, which may involve changes in the mean level and covariance function.},
  author       = {Åke, Björnham and Lindgren, Georg},
  issn         = {0006-3444},
  keyword      = {Estimation of the mean,Level crossings,Mean frequency,Spectral moment,Stationary normal process,Time series estimation},
  language     = {eng},
  number       = {3},
  pages        = {507--512},
  publisher    = {ARRAY(0x961baf8)},
  series       = {Biometrika},
  title        = {Frequency estimation from crossings of an observed mean level},
  url          = {http://dx.doi.org/10.1093/biomet/63.3.507},
  volume       = {63},
  year         = {1976},
}