Optimal Filtering: Volume II: Spatio-Temporal Fields: 481 (Mathematics and Its Applications) - Tapa dura

Fomin, V.N.

 
9780792357346: Optimal Filtering: Volume II: Spatio-Temporal Fields: 481 (Mathematics and Its Applications)
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ISBN 10: 0792357345 ISBN 13: 9780792357346
Editorial: Springer, 1999

Sinopsis

In this volume the investigations of filtering problems, a start on which has been made in [55], are being continued and are devoted to theoretical problems of processing stochastic fields. The derivation of the theory of processing stochastic fields is similar to that of the theory extensively developed for stochastic processes (’stochastic fields with a one-dimensional domain’). Nevertheless there exist essential distinctions between these cases making a construction of the theory for the multi-dimensional case in such a way difficult. Among these are the absence of the notion of the ’past-future’ in the case of fields, which plays a fundamental role in constructing stochastic processes theory. So attempts to introduce naturally the notion of the causality (non-anticipativity) when synthesising stable filters designed for processing fields have not met with success. Mathematically, principal distinctions between multi-dimensional and one-dimensional cases imply that the set of roots of a multi-variable polyno­ mial does not necessary consist of a finite number of isolated points. From the main theorem of algebra it follows that in the one-dimensional case every poly­ nomial of degree n has just n roots (considering their multiplicity) in the com­ plex plane. As a consequence, in particular, an arbitrary rational function ¢(.

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Reseña del editor

In this volume the investigations of filtering problems, a start on which has been made in [55], are being continued and are devoted to theoretical problems of processing stochastic fields. The derivation of the theory of processing stochastic fields is similar to that of the theory extensively developed for stochastic processes ('stochastic fields with a one-dimensional domain'). Nevertheless there exist essential distinctions between these cases making a construction of the theory for the multi-dimensional case in such a way difficult. Among these are the absence of the notion of the 'past-future' in the case of fields, which plays a fundamental role in constructing stochastic processes theory. So attempts to introduce naturally the notion of the causality (non-anticipativity) when synthesising stable filters designed for processing fields have not met with success. Mathematically, principal distinctions between multi-dimensional and one-dimensional cases imply that the set of roots of a multi-variable polyno­ mial does not necessary consist of a finite number of isolated points. From the main theorem of algebra it follows that in the one-dimensional case every poly­ nomial of degree n has just n roots (considering their multiplicity) in the com­ plex plane. As a consequence, in particular, an arbitrary rational function ¢(.

Reseña del editor

This book considers methods for the optimal processing of random fields. In particular, it studies spatio-temporal filtering problems such as the problem of optimal signal detection (Bayes' approach) and estimating angles of arrival of local signals. The exposition of the problem of optimal filtering is presented with the help of insights from probability theory, functional analysis and mathematical physics. An algorithmic form of the net results facilitates computer-aided applications.
Audience: This volume will be of interest to experts in the design of signal processing and theorists in functional analysis, probability theory, functional analysis and mathematical physics.

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Editorial
Springer
Año de publicación
1999
Idioma
Inglés
ISBN 10 
0792357345
ISBN 13 
9780792357346
Encuadernación
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Número de páginas
376
Contacto del fabricante
no disponible
Persona responsable
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Alemania

Otras ediciones populares con el mismo título

9789401059749: Optimal Filtering: Volume II: Spatio-Temporal Fields: 481 (Mathematics and Its Applications)

Edición Destacada

ISBN 10:  9401059748 ISBN 13:  9789401059749
Editorial: Springer, 2012
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