Review of Unbiased FIR Filters, Smoothers, and Predictors for Polynomial Signals

Yuriy S Shmaliy, Yrjö Neuvo, Sanowar Khan

    Research output: Contribution to journalArticleScientificpeer-review


    Extracting an estimate of a slowly varying signal corrupted by noise is a common task. Examples can be found in industrial, scientific and biomedical instrumentation. Depending on the nature of the application the signal estimate is allowed to be a delayed estimate of the original signal or, in the other extreme, no delay is tolerated. These cases are commonly referred to as filtering, prediction, and smoothing depending on the amount of advance or lag between the input data set and the output data set. In this review paper we provide a comprehensive set of design and analysis tools for designing unbiased FIR filters, predictors, and smoothers for slowly varying signals, i.e. signals that can be modeled by low order polynomials. Explicit expressions of parameters needed in practical implementations are given. Real life examples are provided including cases where the method is extended to signals that are piecewise slowly varying. A critical view on recursive implementations of the algorithms is provided.
    Original languageEnglish
    Pages (from-to)1-29
    Number of pages29
    JournalFrontiers in Signal Processing
    Issue number1
    Publication statusPublished - 1 Jan 2018
    MoE publication typeA1 Journal article-refereed


    • Polynomial signal
    • unbiased FIR filter
    • trend analysis
    • signal prediction
    • signal smoothing
    • digital filter design


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