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Theory of Affine Projection Algorithms for Adaptive Filtering

Part of the Mathematics for Industry Book Series (volume 22)

DOI: 10.1007/978-4-431-55738-8

ISBN: 978-4-431-55737-1

Publisher: Springer Japan - Springer Journals

Jul 23, 2015

LitStream

Chapter 1Introduction

Ozeki, Kazuhiko

Pages: 1 –6

[An adaptive filter is a kind of learning machine that changes its transfer function automatically. It has two key components: a transversal filter to process the input signal, and a mechanism to control the coefficients of the transversal filter so that it produces an output signal that...
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Chapter 2Classical Adaptation Algorithms

Ozeki, Kazuhiko

Pages: 7 –13

[In this chapter, two classical adaptation algorithms, the least-mean-squares algorithm (LMS algorithm) and the normalized least-mean-squares algorithm (NLMS algorithm), are reviewed. The LMS algorithm, also known as the Widrow-Hoff algorithm, is motivated by the steepest-descent method to...
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Chapter 3Affine Projection Algorithm

Ozeki, Kazuhiko

Pages: 15 –57

[The normalized least-mean-squares (NLMS) algorithm has a problem that the convergence slows down for correlated input signals. The reason for this phenomenon is explained by looking at the algorithm from a geometrical point of view. This observation motivates the affine projection algorithm...
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Chapter 4Family of Affine Projection Algorithms

Ozeki, Kazuhiko

Pages: 59 –64

[After the birth of the basic affine projection algorithm (B-APA) in the middle of 1980s, several adaptive filtering algorithms that also exploit multiple regressors were put forward independently. They are now recognized as variants of the B-APA, forming a family of affine projection algorithms....
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Chapter 5Convergence Behavior of APA

Ozeki, Kazuhiko

Pages: 65 –119

[The behavior of an adaptive filter depends on the input signal. However, since there are infinitely many variations of signals, it is difficult to draw general, useful conclusions on the behavior of an adaptive filter taking the waveform of each signal into consideration. Therefore, we often...
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Chapter 6Reduction of Computational Complexity

Ozeki, Kazuhiko

Pages: 121 –163

[If a naive method is employed to implement the APA, the number of arithmetic operations per sample is approximately given by a polynomial αp3+βnp2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}...
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Chapter 7Kernel Affine Projection Algorithm

Ozeki, Kazuhiko

Pages: 165 –185

[The unknown system to be identified by an adaptive filter is usually assumed to be a linear system. Based on this assumption, we model the unknown system by a linear filter. In reality, however, there are cases where a linear filter is inadequate. In spite of this problem, using a very general...
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Chapter 8Variable Parameter APAs

Ozeki, Kazuhiko

Pages: 187 –204

[The standard APA has three parameters: the step-size parameter, the projection order, and the regularization factor, which are all assumed to be invariable in the preceding chapters. However, by adjusting those parameters adaptively, it is possible to improve the performance of the APA. This...

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