Isaac Scientific Publishing

Frontiers in Signal Processing

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

Download PDF (1713.2 KB) PP. 1 - 29 Pub. Date: January 17, 2018

DOI: 10.22606/fsp.2018.21001


  • Yuriy S. Shmaliy*
    Electronics Engineering Department, DICIS, Universidad de Guanajuato, Salamanca, Mexico
  • Yrjö Neuvo
    Department of Communications and Networking, Aalto University, Aalto, Finland
  • Sanowar Khan
    Department of Electrical and Electronic Engineering, City, University of London, London EC1V 0HB, UK


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.


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


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