Optimal Filtering: Volume II: Spatio-Temporal Fields
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1999
|
| Schriftenreihe: | Mathematics and Its Applications
481 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 ¢( |
| Beschreibung: | 1 Online-Ressource (XII, 359 p) |
| ISBN: | 9789401146913 9789401059749 |
| DOI: | 10.1007/978-94-011-4691-3 |
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| 500 | |a 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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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-011-4691-3 |
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| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401146913 9789401059749 |
| language | English |
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| spelling | Fomin, Vladimir Verfasser aut Optimal Filtering Volume II: Spatio-Temporal Fields by Vladimir Fomin Dordrecht Springer Netherlands 1999 1 Online-Ressource (XII, 359 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 481 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 ¢( Mathematics Operator theory Systems theory Engineering design Applications of Mathematics Information and Communication, Circuits Operator Theory Systems Theory, Control Engineering Design Mathematik https://doi.org/10.1007/978-94-011-4691-3 Verlag Volltext |
| spellingShingle | Fomin, Vladimir Optimal Filtering Volume II: Spatio-Temporal Fields Mathematics Operator theory Systems theory Engineering design Applications of Mathematics Information and Communication, Circuits Operator Theory Systems Theory, Control Engineering Design Mathematik |
| title | Optimal Filtering Volume II: Spatio-Temporal Fields |
| title_auth | Optimal Filtering Volume II: Spatio-Temporal Fields |
| title_exact_search | Optimal Filtering Volume II: Spatio-Temporal Fields |
| title_full | Optimal Filtering Volume II: Spatio-Temporal Fields by Vladimir Fomin |
| title_fullStr | Optimal Filtering Volume II: Spatio-Temporal Fields by Vladimir Fomin |
| title_full_unstemmed | Optimal Filtering Volume II: Spatio-Temporal Fields by Vladimir Fomin |
| title_short | Optimal Filtering |
| title_sort | optimal filtering volume ii spatio temporal fields |
| title_sub | Volume II: Spatio-Temporal Fields |
| topic | Mathematics Operator theory Systems theory Engineering design Applications of Mathematics Information and Communication, Circuits Operator Theory Systems Theory, Control Engineering Design Mathematik |
| topic_facet | Mathematics Operator theory Systems theory Engineering design Applications of Mathematics Information and Communication, Circuits Operator Theory Systems Theory, Control Engineering Design Mathematik |
| url | https://doi.org/10.1007/978-94-011-4691-3 |
| work_keys_str_mv | AT fominvladimir optimalfilteringvolumeiispatiotemporalfields |