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

Abstract

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.

ECG Signal Denoising and Features Extraction Using Unbiased FIR Smoothing

“…Even so, there are some zones in the ECG picture where linear predictors are unsuccessful in extracting ECG features. Therefore, a comparative analysis of different methods developed in [36–39] is required.…”

“…A special case of the p -shift OFIR filter is the p -shift unbiased FIR (UFIR) filter [36–39], which completely ignores zero mean noise and is thus more suitable for ECG signals. As being more general, the p -shift UFIR filter generalizes the Savitzky-Golay filter by p = −( N − 1)/2 and linear predictor with p > 0.…”