Advanced Topics in System and Signal Theory

A Mathematical Approach

  • Volker Pohl
  • Holger Boche
Part of the Foundations in Signal Processing, Communications and Networking book series (SIGNAL, volume 4)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Mathematical Preliminaries

    1. Front Matter
      Pages 1-1
  3. Part I Mathematical Preliminaries

    1. Volker Pohl, Holger Boche
      Pages 3-14
    2. Volker Pohl, Holger Boche
      Pages 15-50
    3. Volker Pohl, Holger Boche
      Pages 51-66
    4. Volker Pohl, Holger Boche
      Pages 67-78
  4. Fundamental Operators

    1. Front Matter
      Pages 79-79
  5. Part II Fundamental Operators

    1. Volker Pohl, Holger Boche
      Pages 81-98
    2. Volker Pohl, Holger Boche
      Pages 99-118
  6. Causality Aspects in Signal and System Theory

    1. Front Matter
      Pages 119-119
  7. Part III Causality Aspects in Signal and System Theory

    1. Volker Pohl, Holger Boche
      Pages 121-136
    2. Volker Pohl, Holger Boche
      Pages 137-151
    3. Volker Pohl, Holger Boche
      Pages 153-162
    4. Volker Pohl, Holger Boche
      Pages 163-232
  8. Back Matter
    Pages 1-8

About this book

Introduction

This book provides an in-depth analysis of selected methods in signal and system theory with applications to problems in communications, stochastic processes and optimal filter theory. The authors take a consistent functional analysis and operator theoretic approach to linear system theory, using Banach algebra and Hardy space techniques. The themes connecting all the chapters are questions concerning the consequences of the causality constraint, which is necessary in all realizable systems, and the question of robustness of linear systems with respect to errors in the data.

The first part of the book contains basic background on the necessary mathematical tools and provides a basic foundation of signal and system theory. Emphasis is given to the close relation between properties of linear systems such as causality, time-invariance, and robustness on the one hand and the algebraic structures and analytic properties of the mathematical objects, such as Banach algebras or Hardy spaces, on the other hand. The requirement of causality in system theory is inevitably accompanied by the appearance of certain mathematical operations, namely the Riesz projection and the Hilbert transform. These operations are studied in detail in part two. Part three relates the mathematical techniques that are developed in the first two parts to the behaviour of linear systems that are of interest from an engineering perspective, such as expansions of transfer functions in orthonormal bases, the approximation from measured data and the numerical calculation of the Hilbert transform, as well as spectral factorization.

Keywords

Multi-Antenna Systems Packet Radio Networks QoS Opimization Quality of Service Radio Access Networks Scheduling Signal Processing communication system systems theory

Authors and affiliations

  • Volker Pohl
    • 1
  • Holger Boche
    • 2
  1. 1.Nachrichtentechnik, Heinrich-Hertz-Inst.Fraunhofer-Institut fürBerlinGermany
  2. 2.Nachrichtentechnik, Heinrich-Hertz-Inst.Fraunhofer-Institut fürBerlinGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-03639-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-642-03638-5
  • Online ISBN 978-3-642-03639-2
  • Series Print ISSN 1863-8538
  • Series Online ISSN 1863-8546