A Rapid Introduction to Adaptive Filtering

  • Leonardo Rey Vega
  • Hernan Rey

Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Leonardo Rey Vega, Hernan Rey
    Pages 1-5
  3. Leonardo Rey Vega, Hernan Rey
    Pages 7-17
  4. Leonardo Rey Vega, Hernan Rey
    Pages 19-31
  5. Leonardo Rey Vega, Hernan Rey
    Pages 33-88
  6. Leonardo Rey Vega, Hernan Rey
    Pages 89-112
  7. Leonardo Rey Vega, Hernan Rey
    Pages 113-119
  8. Back Matter
    Pages 121-122

About this book


In this book, the authors provide insights into the basics of adaptive filtering, which are particularly useful for students taking their first steps into this field. They start by studying the problem of minimum mean-square-error filtering, i.e., Wiener filtering. Then, they analyze iterative methods for solving the optimization problem, e.g., the Method of Steepest Descent. By proposing stochastic approximations, several basic adaptive algorithms are derived, including Least Mean Squares (LMS), Normalized Least Mean Squares (NLMS) and Sign-error algorithms. The authors provide a general framework to study the stability and steady-state performance of these algorithms. The affine Projection Algorithm (APA) which provides faster convergence at the expense of computational complexity (although fast implementations can be used) is also presented. In addition, the Least Squares (LS) method and its recursive version (RLS), including fast implementations are discussed. The book closes with the discussion of several topics of interest in the adaptive filtering field.


APA Affine Projection Algorithms Computational Complexity LMS Least Mean Squares LS Least Squares and RLS Recursive Least Squares NLMS Normalized Mean Squares Sign-error Algorithm Stochastic Gradient Adaptive Filtering Wiener Filtering steepest Descent Procedures

Authors and affiliations

  • Leonardo Rey Vega
    • 1
  • Hernan Rey
    • 2
  1. 1., School of EngineeringUniversity of Buenos AiresBuenos AiresArgentina
  2. 2., Department of EngineeringUniversity of LeicesterLeicesterUnited Kingdom

Bibliographic information

  • DOI
  • Copyright Information The Author(s) 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-642-30298-5
  • Online ISBN 978-3-642-30299-2
  • Series Print ISSN 2191-8112
  • Series Online ISSN 2191-8120
  • Buy this book on publisher's site