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**Synopsis:** 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 .

**From the 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.

Title: **Advanced Topics in System and Signal Theory:...**

Publisher: **Springer**

Publication Date: **2009**

Binding: **Hardcover**

Book Condition: **Used: Good**

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**Book Description **Springer, 2016. Paperback. Book Condition: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Bookseller Inventory # ria9783642036385_lsuk

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**Book Description **Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, 2009. HRD. Book Condition: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Bookseller Inventory # IP-9783642036385

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**Book Description **Springer-Verlag Gmbh Okt 2009, 2009. Buch. Book Condition: Neu. Neuware - 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 . 241 pp. Englisch. Bookseller Inventory # 9783642036385

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Published by
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ISBN 10: 3642036384
ISBN 13: 9783642036385

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**Book Description **Springer-Verlag Gmbh Okt 2009, 2009. Buch. Book Condition: Neu. Neuware - 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 . 241 pp. Englisch. Bookseller Inventory # 9783642036385

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Published by
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ISBN 10: 3642036384
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**Book Description **Springer-Verlag Gmbh Okt 2009, 2009. Buch. Book Condition: Neu. Neuware - 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 . 241 pp. Englisch. Bookseller Inventory # 9783642036385

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Published by
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ISBN 10: 3642036384
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**Book Description **Springer-Verlag Gmbh Okt 2009, 2009. Buch. Book Condition: Neu. Neuware - 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 . 241 pp. Englisch. Bookseller Inventory # 9783642036385

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