Generalized Hampel Filters

Ronald K. Pearson, Yrjö Neuvo, Jaakko Astola, Moncef Gabbouj

    Research output: Contribution to journalArticleScientificpeer-review

    64 Citations (Scopus)
    1400 Downloads (Pure)

    Abstract

    The standard median filter based on a symmetric moving window has only one tuning parameter: the window width. Despite this limitation, this filter has proven extremely useful and has motivated a number of extensions: weighted median filters, recursive median filters, and various cascade structures. The Hampel filter is a member of the class of decsion filters that replaces the central value in the data window with the median if it lies far enough from the median to be deemed an outlier. This filter depends on both the window width and an additional tuning parameter t, reducing to the median filter when t=0, so it may be regarded as another median filter extension. This paper adopts this view, defining and exploring the class of generalized Hampel filters obtained by applying the median filter extensions listed above: weighted Hampel filters, recursive Hampel filters, and their cascades. An important concept introduced here is that of an implosion sequence, a signal for which generalized Hampel filter performance is independent of the threshold parameter t. These sequences are important because the added flexibility of the generalized Hampel filters offers no practical advantage for implosion sequences. Partial characterization results are presented for these sequences, as are useful relationships between root sequences for generalized Hampel filters and their median-based counterparts. To illustrate the performance of this filter class, two examples are considered: one is simulation-based, providing a basis for quantitative evaluation of signal recovery performance as a function of t, while the other is a sequence of monthly Italian industrial production index values that exhibits glaring outliers.

    Original languageEnglish
    Article number87
    JournalEurasip Journal on Advances in Signal Processing
    Volume2016
    Issue number1
    DOIs
    Publication statusPublished - 1 Dec 2016
    Publication typeA1 Journal article-refereed

    Publication forum classification

    • Publication forum level 1

    ASJC Scopus subject areas

    • Hardware and Architecture
    • Signal Processing
    • Electrical and Electronic Engineering

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