Overview
- Gives a concise picture of the mathematical foundations of network calculus
- Basic treatment of Quality-of-Service Optimization
- Includes supplementary material: sn.pub/extras
Part of the book series: Foundations in Signal Processing, Communications and Networking (SIGNAL, volume 4)
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About this book
The requirement of causality in system theory is inevitably accompanied by the appearance of certain mathematical operations, namely the Riesz proj- tion,theHilberttransform,andthespectralfactorizationmapping.Aclassical exampleillustratingthisisthedeterminationoftheso-calledWiener?lter(the linear, minimum means square error estimation ?lter for stationary stochastic sequences [88]). If the ?lter is not required to be causal, the transfer function of the Wiener ?lter is simply given by H(?)=? (?)/? (?),where ? (?) xy xx xx and ? (?) are certain given functions. However, if one requires that the - xy timation ?lter is causal, the transfer function of the optimal ?lter is given by 1 ? (?) xy H(?)= P ,?? (??,?] . + [? ] (?) [? ] (?) xx + xx? Here [? ] and [? ] represent the so called spectral factors of ? ,and xx + xx? xx P is the so called Riesz projection. Thus, compared to the non-causal ?lter, + two additional operations are necessary for the determination of the causal ?lter, namely the spectral factorization mapping ? ? ([? ] ,[? ] ),and xx xx + xx? the Riesz projection P .
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Table of contents (10 chapters)
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Front Matter
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Mathematical Preliminaries
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Front Matter
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Part I Mathematical Preliminaries
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Fundamental Operators
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Front Matter
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Part II Fundamental Operators
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Causality Aspects in Signal and System Theory
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Front Matter
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Part III Causality Aspects in Signal and System Theory
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Back Matter
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)
Authors and Affiliations
Bibliographic Information
Book Title: Advanced Topics in System and Signal Theory
Book Subtitle: A Mathematical Approach
Authors: Volker Pohl, Holger Boche
Series Title: Foundations in Signal Processing, Communications and Networking
DOI: https://doi.org/10.1007/978-3-642-03639-2
Publisher: Springer Berlin, Heidelberg
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2010
Hardcover ISBN: 978-3-642-03638-5Published: 16 October 2009
Softcover ISBN: 978-3-642-26096-4Published: 14 March 2012
eBook ISBN: 978-3-642-03639-2Published: 03 October 2009
Series ISSN: 1863-8538
Series E-ISSN: 1863-8546
Edition Number: 1
Number of Pages: VIII, 241
Number of Illustrations: 5 b/w illustrations
Topics: Communications Engineering, Networks, Computer Engineering, Computer Communication Networks, Algorithms, Mathematical and Computational Engineering, Computer Systems Organization and Communication Networks