Adaptive Filtering Algorithms and Practical Implementation

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Paulo s.r. diniz Adaptive Filtering Algorithms and Practical Implementation Fourth edition ② Springer Paulo s.r. diniz Universidade federal do rio de janeiro Rio de janeiro. brazi diniz @lps. ufri br ISBN978-1-4614-4105-2 ISBN978-1-46144106-9( e Book) DOⅠ10.1007/978-1-46144106-9 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012942860 o Springer science+ Business media New York 1997. 2002. 2008. 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection ith reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publishers location, in its current version, and permission for use must always be obtained from Springer Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Lay The use of general descriptive names, registered names, trademarks, service markS, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein Printed on acid-free paper SpringerispartofSpringerScience+businessMedia( To: My Parents, Mariza, Paula, and luiza Preface The field of Digital Signal Processing has developed so fast in the last 3 decades that it can be found in the graduate and undergraduate programs of most uni versities. This development is related to the increasingly available technologies for implementing digital signal processing algorithms. The tremendous growth of development in the digital signal processing area has turned some of its specialized areas into fields themselves. If accurate information of the signals to be processed is available, the designer can easily choose the most appropriate algorithm to process the signal. When dealing with signals whose statistical properties are unknown, fixed algorithms do not process these signals efficiently. The solution is to use an adaptive filter that automatically changes its characteristics by optimizing the internal parameters. The adaptive filtering algorithms are essential in many statistical signal processing applications. Although the field of adaptive signal processing has been the subject of research for over 4 decades, it was in the eighties that a major growth occurred in research and applications. two main reasons can be credited to this growth: the availability of im plementation tools and the appearance of early textbooks exposing the subject in an organized manner. Still today it is possible to observe many research developments in the area of adaptive filtering, particularly addressing specific applications. In fact, the theory of linear adaptive filtering has reached a maturity that justifies a text treating the various methods in a unified way, emphasizing the algorithms suitable for practical implementation. This text concentrates on studying online algorithms those whose adaptation occurs whenever a new sample of each environment signal iS available. The so-called block algorithms, those whose adaptation occurs when a new block of data is available are also included using the subband filtering framework. Usually, block algorithms require different implementation resources than online algorithms This book also includes basic introductions to nonlinear adaptive filtering and blind signal processing as natural extensions of the algorithms treated in the earlier chapters. The understanding of the introductory material presented is fundamental for further studies in these fields which are described in more detail in some specialized texts P rerace The idea of writing this book started while teaching the adaptive signal process- ing course at the graduate school of the Federal University of rio de janeiro UFRn) The request of the students to cover as many algorithms as possible made me think how to organize this subject such that not much time is lost in adapting notations and derivations related to different algorithms. Another common question was which algorithms really work in a finite-precision implementation. These issues led me to conclude that a new text on this subject could be written with these objectives in mind. Also, considering that most graduate and undergraduate programs include a single adaptive filtering course, this book should not be lengthy. Although the current version of the book is not short, the first six chapters contain the core of the subject matter. Another objective to seek is to provide an easy access to the working algorithms for the practitioner. It was not until I spent a sabbatical year and a half at University of victoria, Canada, that this project actually started. In the leisure hours, I slowly started this project. Parts of the early chapters of this book were used in short courses on adap- tive signal processing taught at different institutions, namely: Helsinki University of Technology(renamed as Aalto University), Espoo, Finland; University Menendez Pelayo in Seville, Spain; and the Victoria Micronet Center, University of victoria Canada. The remaining parts of the book were written based on notes of the graduate course in adaptive signal processing taught at COPPE (the graduate engineering school of UFRD) The philosophy of the presentation is to expose the material with a solid theoretical foundation, while avoiding straightforward derivations and repetition The idea is to keep the text with a manageable size, without sacrificing clarity and without omitting important subjects. Another objective is to bring the reader up to the point where implementation can be tried and research can begin. A number of references are included at the end of the chapters in order to aid the reader to proceed on learning the subject It is assumed the reader has previous background on the basic principles of digital signal processing and stochastic processes, including: discrete-time Fourier- and z-transforms, finite impulse response(FIr) and infinite impulse response (IIr) digital filter realizations, multirate systems, random variables and processes, first- and second-order statistics, moments, and filtering of random signals. Assuming that the reader has this background, I believe the book is self-contained Chapter I introduces the basic concepts of adaptive filtering and sets a general framework that all the methods presented in the following chapters fall under. A brief introduction to the typical applications of adaptive filtering is also presented In Chap. 2, the basic concepts of discrete-time stochastic processes are reviewed with special emphasis on the results that are useful to analyze the behavior of adaptive filtering algorithms. In addition, the Wiener filter is presented, establishing the optimum linear filter that can be sought in stationary environments. Chapter 14 briefly describes the concepts of complex differentiation mainly applied to the Wiener solution. The case of linearly constrained Wiener filter is also discussed motivated by its wide use in antenna array processing. The transformation of the constrained minimization problem into an unconstrained one is also presented Preface The concept of mean-square error surface is then introduced, another useful tool to analyze adaptive filters. The classical Newton and steepest-descent algorithms are briefly introduced. Since the use of these algorithms would require a com- plete knowledge of the stochastic environment, the adaptive filtering algorithms introduced in the following chapters come into play. Practical applications of the adaptive filtering algorithms are revisited in more detail at the end of Chap 2 where some examples with closed form solutions are included in order to allow the correct interpretation of what is expected from each application Chapter 3 presents and analyzes the least-mean-square (LMs)algorithm in some depth. Several aspects are discussed, such as convergence behavior in stationary and nonstationary environments. This chapter also includes a number of theoretical as well as simulation examples to illustrate how the lms algorithm performs in different setups. Chapter 15 addresses the quantization effects on the lms algorithm when implemented in fixed-and floating-point arithmetic Chapter 4 deals with some algorithms that are in a sense related to the lms al gorithm. In particular, the algorithms introduced are the quantized-error algorithms, the lms-Newton algorithm, the normalized lms algorithm, the transform-domain LMS algorithm, and the affine projection algorithm. Some properties of these algorithms are also discussed in Chap 4, with special emphasis on the analysis of the affine projection algorithm Chapter 5 introduces the conventional recursive least-squares(RLs)algorithm This algorithm minimizes a deterministic objective function, differing in this sense from most LMS-based algorithms. Following the same pattern of presentation of Chap 3, several aspects of the conventional RLS algorithm are discussed, such as convergence behavior in stationary and nonstationary environments along with a number of simulation results. Chapter 16 deals with stability issues and quantization effects related to the rls algorithm when implemented in fixed- and floating-point rithmetic. The results presented, except for the quantization effects are also valid for the rls algorithms presented in Chaps. 7-9. As a complement to Chap 5 Chap. 17 presents the discrete-time Kalman filter formulation which, despite being considered an extension of the wiener filter. has some relation with the rls algorithm Chapter 6 discusses some techniques to reduce the overall computational com- plexity of adaptive filtering algorithms. The chapter first introduces the so-called set-membership algorithms that update only when the output estimation error is higher than a prescribed upper bound. However, since set-membership algorithms require frequent updates during the early iterations in stationary environments, we introduce the concept of partial update to reduce the computational complexity in order to deal with situations where the available computational resources are scarce. In addition, the chapter presents several forms of set-membership algorithms related to the affine projection algorithms and their special cases. Chapter 18 briefly presents some closed-form expressions for the excess Mse and the conver- gence time constants of the simplified set-membership affine projection algorithm Chapter 6 also includes some simulation examples addressing standard as well as

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