Advanced Topics in System and Signal Theory: A Mathematical Approach by Volker P

The Nile on eBay   FREE SHIPPING UK WIDE   Advanced Topics in System and Signal Theory by Volker Pohl, Holger Boche

(?) xy xx xx and ? However, if one requires that the - xy timation ?lter is causal, the transfer function of the optimal ?lter is given by 1 ? ] (?) [? ] (?) xx + xx? ] and [? ] represent the so called spectral factors of ? ] ),and xx xx + xx?

FORMATHardcover LANGUAGEEnglish CONDITIONBrand New Publisher Description

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 .

Notes

Gives a concise picture of the mathematical foundations of network calculusBasic treatment of Quality-of-Service Optimization

Back Cover

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.

Table of Contents

I Mathematical Preliminaries.- Function Spaces and Operators.- Fourier Analysis and Analytic Functions.- Banach Algebras.- Signal Models and Linear Systems.- II Fundamental Operators.- Poisson Integral and Hilbert Transformation.- Causal Projections.- III Causality Aspects in Signal and System Theory.- Disk Algebra Bases.- Causal Approximations.- On Algorithms for Calculating the Hilbert Transform.- Spectral Factorization.

Review

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)

Long Description

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 .

Review Quote

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)

Feature

Gives a concise picture of the mathematical foundations of network calculus Basic treatment of Quality-of-Service Optimization

Details ISBN3642036384 Author Holger Boche Short Title ADVD TOPICS IN SYSTEM & SIGNAL Language English ISBN-10 3642036384 ISBN-13 9783642036385 Media Book Format Hardcover Series Number 4 Year 2009 Pages 241 Series Foundations in Signal Processing, Communications and Networking Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany DEWEY 621.38223 Subtitle A Mathematical Approach DOI 10.1007/978-3-642-03639-2 Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Edition Description 2010 ed. Edition 2010th Publication Date 2009-10-16 Alternative 9783642260964 Illustrations 5 Illustrations, black and white; VIII, 241 p. 5 illus. Audience Professional & Vocational We've got this

At The Nile, if you're looking for it, we've got it.With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love!

30 DAY RETURN POLICY

No questions asked, 30 day returns!

FREE DELIVERY

No matter where you are in the UK, delivery is free.

SECURE PAYMENT

Peace of mind by paying through PayPal and eBay Buyer Protection TheNile_Item_ID:137566049;