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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.
- Sales Rank: #1389986 in Books
- Brand: Brand: Birkhäuser
- Published on: 1997-12-18
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x .69" w x 6.14" l, 1.30 pounds
- Binding: Hardcover
- 284 pages
- Used Book in Good Condition
Review
"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
About the Author
Tolimieri-CCNY/CUNY, New York
Myoung-A.J. Devaney Associates, Boston, MA
Most helpful customer reviews
2 of 2 people found the following review helpful.
The Best Pure/Applied Math Book
By wjd
The is one of the best math books I've ever read. The reason is simple: the presentation is elegant and abstract, yet remains remarkably useful for applications. Tolimieri and An present a consice language in which to describe and use the mathematical entities underlying modern Fourier methods. In this language, many of the deep connections of this subject are reduced to trivial one line proofs. It's quite an amazing book. I wouldn't necessarily recommend it as an introduction to Fourier or Time-Frequency analysis -- especially if you're an engineer, or one who avoids abstract math -- but if you're looking for a nice, elegant treatment, this is the book you need.
0 of 0 people found the following review helpful.
Excelente Book
By psoto
This book is excellent for people that study Signal Processing or Applied Mathematics. The book has a little bump, but it does not matter.
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