Foundations in Signal Processing, Communications and Networking

Advanced Topics in System and Signal Theory

A Mathematical Approach

Authors: Pohl, Volker, Boche, Holger

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About this book

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.

Reviews

From the reviews:

“It is intended primarily for engineers working in the area of robustness problems under a casualty constraint. At the beginning it presents the mathematical methods, necessary to approaching theses problems. Then, some related classical results concerning the boundedness and continuity of the Hilbert transform and Riesz projection are presented. Finally, these methods and results are applied to selected topics from signal processing.” (Tzvetan Semerdjiev, Zentralblatt MATH, Vol. 1179, 2010)

“The monograph gives an elaborate treatment of some tools used in signal and system theory, which have applications in communications, stochastic processes and optimal filter theory. … Appropriate references are provided for the reader interested in details. … The book is a valuable addition to the mathematical literature related to signal processing, and should be useful to students in engineering as well as to mathematicians interested in applications.”­­­ (Amol J. Sasane, Mathematical Reviews, Issue 2010 j)


Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $129.00
price for USA in USD
  • ISBN 978-3-642-03639-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.99
price for USA in USD
  • ISBN 978-3-642-03638-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $169.99
price for USA in USD
  • ISBN 978-3-642-26096-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Advanced Topics in System and Signal Theory
Book Subtitle
A Mathematical Approach
Authors
Series Title
Foundations in Signal Processing, Communications and Networking
Series Volume
4
Copyright
2010
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-03639-2
DOI
10.1007/978-3-642-03639-2
Hardcover ISBN
978-3-642-03638-5
Softcover ISBN
978-3-642-26096-4
Series ISSN
1863-8538
Edition Number
1
Number of Pages
VIII, 241
Number of Illustrations
5 b/w illustrations
Topics