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Linear Prediction Theory

A Mathematical Basis for Adaptive Systems

  • Book
  • © 1990

Overview

Authors:
  1. Peter Strobach

    1. ZFE IS — Forschung für Informatik und Software, SIEMENS AG, Zentralabteilung Forschung und Entwicklung, München 83, Fed. Rep. of Germany

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Part of the book series: Springer Series in Information Sciences (SSINF, volume 21)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-XVI
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  2. Introduction

    • Peter Strobach
    Pages 1-12

  3. The Linear Prediction Model

    • Peter Strobach
    Pages 13-36

  4. Classical Algorithms for Symmetric Linear Systems

    • Peter Strobach
    Pages 37-62

  5. Recursive Least-Squares Using the QR Decomposition

    • Peter Strobach
    Pages 63-101

  6. Recursive Least-Squares Transversal Algorithms

    • Peter Strobach
    Pages 102-157

  7. The Ladder Form

    • Peter Strobach
    Pages 158-196

  8. Levinson-Type Ladder Algorithms

    • Peter Strobach
    Pages 197-233

  9. Covariance Ladder Algorithms

    • Peter Strobach
    Pages 234-280

  10. Fast Recursive Least-Squares Ladder Algorithms

    • Peter Strobach
    Pages 281-311

  11. Special Signal Models and Extensions

    • Peter Strobach
    Pages 312-335

  12. Concluding Remarks and Applications

    • Peter Strobach
    Pages 336-340

  13. Back Matter

    Pages 341-422
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Keywords

About this book

Lnear prediction theory and the related algorithms have matured to the point where they now form an integral part of many real-world adaptive systems. When it is necessary to extract information from a random process, we are frequently faced with the problem of analyzing and solving special systems of linear equations. In the general case these systems are overdetermined and may be characterized by additional properties, such as update and shift-invariance properties. Usually, one employs exact or approximate least-squares methods to solve the resulting class of linear equations. Mainly during the last decade, researchers in various fields have contributed techniques and nomenclature for this type of least-squares problem. This body of methods now constitutes what we call the theory of linear prediction. The immense interest that it has aroused clearly emerges from recent advances in processor technology, which provide the means to implement linear prediction algorithms, and to operate them in real time. The practical effect is the occurrence of a new class of high-performance adaptive systems for control, communications and system identification applications. This monograph presumes a background in discrete-time digital signal processing, including Z-transforms, and a basic knowledge of discrete-time random processes. One of the difficulties I have en­ countered while writing this book is that many engineers and computer scientists lack knowledge of fundamental mathematics and geometry.

Authors and Affiliations

  • ZFE IS — Forschung für Informatik und Software, SIEMENS AG, Zentralabteilung Forschung und Entwicklung, München 83, Fed. Rep. of Germany

    Peter Strobach

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