Principles and Applications of Adaptive Filters: A Tutorial Review,

摘要

This report reviews the characteristics of a class of adaptive filters useful in signal processing and other applications where the properties of the signal are unknown or variable with time. The basic element of these filters is the adpative linear combiner, which weights (adjusts the gain of) and sums a set of input signals to form a single output signal. The weighting process is governed by a recursive algorithm that seeks to minimize the mean square of the difference between the combiner's output and a 'desired response' (training signal). It is shown that for statistically stationary inputs the mean-square difference is a quadratic function of the weight values, allowing the minimum to be sought by gradient estimation and other similar techniques. Expressions are given that define the relationship between rate of adaptation and deviation from optimal performance due to noise in the gradient estimation process for the Widrow-Hoff LMS algorithm. Methods of deriving the inputs to the combiner are described, including the use of a tapped delay line to form an adaptive transversal filter. Experimental results obtained by computer simulation are presented that show the ability of the adaptive transversal filter to model an unknown network or physical system; to reduce or eliminate intersymbol interference in multipath communication channels; to reduce or eliminate periodic interference in electrocardiography and broadband interference in the sidelobes of an antenna array; and to separate periodic and broadband signals and detect very low level periodic signals. (Author)