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Optimal Filtering : Optimal Filtering Spatio-temporal Fields v. 2 - Vladimir M. Fomin

Optimal Filtering

Optimal Filtering Spatio-temporal Fields v. 2

Hardcover Published: 31st May 1999
ISBN: 9780792357346
Number Of Pages: 359

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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 ¢(.

Preface
Fields and means of describing them
Models of continuous fields and associated problems
Filtering of spatio-temporal fields
Optimal filtering of discrete homogeneous fields
Fields in electrodynamics
Spectral analysis of time series
Spectral analysis of discrete homogeneous fields
References
Notation
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780792357346
ISBN-10: 0792357345
Series: Mathematics and Its Applications : Book 2
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 359
Published: 31st May 1999
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.4 x 17.0  x 2.2
Weight (kg): 1.55