Optimal Filtering : Volume II: Spatio-Temporal Fields

V. N. Fomin

ISBN 10: 9401059748 / ISBN 13: 9789401059749

Verlag: Springer Netherlands, Springer Netherlands, 2012

Beschreibung

Druck auf Anfrage Neuware - Printed after ordering - 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 Ct. (.

Bestandsnummer des Verkäufers 9789401059749

Bibliografische Details

• Titel: Optimal Filtering : Volume II: Spatio-Temporal Fields
• Verlag: Springer Netherlands, Springer Netherlands
• Erscheinungsjahr: 2012
• Sprache: Englisch
• ISBN-10: 9401059748
• ISBN-13: 9789401059749
• Einband: Taschenbuch
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

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.