Time-Frequency Representations (Applied and Numerical Harmonic Analysis) - Couverture rigide

Livre 2 sur 88: Applied and Numerical Harmonic Analysis

An, Myoung; Tolimieri, Richard

 
9780817639181: Time-Frequency Representations (Applied and Numerical Harmonic Analysis)
Couverture rigide
ISBN 10 : 0817639187 ISBN 13 : 9780817639181
Editeur : Birkhäuser, 1997

Synopsis

The aim of this work is to present several topics in time-frequency analysis as subjects in abelian group theory. The algebraic point of view pre­ dominates as questions of convergence are not considered. Our approach emphasizes the unifying role played by group structures on the development of theory and algorithms. This book consists of two main parts. The first treats Weyl-Heisenberg representations over finite abelian groups and the second deals with mul­ tirate filter structures over free abelian groups of finite rank. In both, the methods are dimensionless and coordinate-free and apply to one and multidimensional problems. The selection of topics is not motivated by mathematical necessity but rather by simplicity. We could have developed Weyl-Heisenberg theory over free abelian groups of finite rank or more generally developed both topics over locally compact abelian groups. However, except for having to dis­ cuss conditions for convergence, Haar measures, and other standard topics from analysis the underlying structures would essentially be the same. A re­ cent collection of papers [17] provides an excellent review of time-frequency analysis over locally compact abelian groups. A further reason for limiting the scope of generality is that our results can be immediately applied to the design of algorithms and codes for time­ frequency processing.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Críticas

"On the one side, the book seems to be dedicated to theory-interested specialists in the area of harmonic analysis, on the other side the last chapter shows that highly theoretical constructs can efficiently be used in modern applications." ―Simulation News Europe

"[The book], devoted to the subject of time-frequency representation, shows that there are still many interesting and useful aspects of Gabor analysis, in particular, in the discrete setting." ―Zentralblatt Math

 

Reseña del editor

The aim of this work is to present several topics in time-frequency analysis as subjects in abelian group theory. The algebraic point of view pre­ dominates as questions of convergence are not considered. Our approach emphasizes the unifying role played by group structures on the development of theory and algorithms. This book consists of two main parts. The first treats Weyl-Heisenberg representations over finite abelian groups and the second deals with mul­ tirate filter structures over free abelian groups of finite rank. In both, the methods are dimensionless and coordinate-free and apply to one and multidimensional problems. The selection of topics is not motivated by mathematical necessity but rather by simplicity. We could have developed Weyl-Heisenberg theory over free abelian groups of finite rank or more generally developed both topics over locally compact abelian groups. However, except for having to dis­ cuss conditions for convergence, Haar measures, and other standard topics from analysis the underlying structures would essentially be the same. A re­ cent collection of papers [17] provides an excellent review of time-frequency analysis over locally compact abelian groups. A further reason for limiting the scope of generality is that our results can be immediately applied to the design of algorithms and codes for time­ frequency processing.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Birkhäuser
Date d'édition
1997
Langue
anglais
ISBN 10 
0817639187
ISBN 13 
9780817639181
Reliure
Tapa dura
Nombre de pages
304
Coordonnées du fabricant
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Allemagne

Autres éditions populaires du même titre

9781461286769: Time-Frequency Representations

Edition présentée

ISBN 10 :  146128676X ISBN 13 :  9781461286769
Editeur : Birkhäuser, 2012
Couverture souple