Modified repeated median filters
AbstractWe discuss moving window techniques for fast extraction of a signal comprising monotonic trends and abrupt shifts from a noisy time series with irrelevant spikes. Running medians remove spikes and preserve shifts, but they deteriorate in trend periods. Modified trimmed mean filters use a robust scale estimate such as the median absolute deviation about the median (MAD) to select an adaptive amount of trimming. Application of robust regression, particularly of the repeated median, has been suggested for improving upon the median in trend periods. We combine these ideas and construct modified filters based on the repeated median offering better shift preservation. All these filters are compared w.r.t. fundamental analytical properties and in basic data situations. An algorithm for the update of the MAD running in time O(log n) for window width n is presented as well. --
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Bibliographic InfoPaper provided by Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen in its series Technical Reports with number 2004,46.
Date of creation: 2004
Date of revision:
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signal extraction; robust filtering; drifts; jumps; outliers; computational geometry; update algorithm;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Fried, Roland & Bernholt, Thorsten & Gather, Ursula, 2004. "Repeated median and hybrid filters," Technical Reports 2004,10, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
- Fried, Roland & Gather, Ursula, 2004. "Methods and algorithms for robust filtering," Technical Reports 2004,44, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
- Gather, Ursula & Fried, Roland & Lanius, Vivian, 2005. "Robust detail-preserving signal extraction," Technical Reports 2005,54, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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