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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1273150
- author
- Åke, Björnham
and Lindgren, Georg
LU
- publishing date
- 1976
- 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
- Oxford University Press
- 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
- 2016-04-04 09:43:07
- date last changed
- 2025-04-04 15:09:10
@article{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}},
keywords = {{Estimation of the mean; Level crossings; Mean frequency; Spectral moment; Stationary normal process; Time series estimation}},
language = {{eng}},
number = {{3}},
pages = {{507--512}},
publisher = {{Oxford University Press}},
series = {{Biometrika}},
title = {{Frequency estimation from crossings of an observed mean level}},
url = {{http://dx.doi.org/10.1093/biomet/63.3.507}},
doi = {{10.1093/biomet/63.3.507}},
volume = {{63}},
year = {{1976}},
}