Time-Frequency Representations / Edition 1

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Time-Frequency Representations provides a fundamental survey of time-frequency representations over finite and finitely generated abelian groups that can be used to design algorithms for multi-dimensional applications. Emphasis is placed on Weyl-Heisenberg systems and expansions. Algorithms are developed within this abstract setting without reference to coordinates or dimension, allowing the derivation of new algorithmic structures with significant importance to multidimensional problems and applications. In addition, tensor product representation is fully developed for the modeling of time-frequency computations. This new book is an excellent text/reference for all computer scientists, computational mathematicians, and electrical engineers who need to understand the foundations of time-frequency representations and their use for multidimensional computations.
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Editorial Reviews

From the Publisher
"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

Presents several topics in time-frequency analysis as subjects in abelian group theory, including linear algebra and abelian groups, poisson summation formula, Weyl-Heisenberg systems, duality, and multirate structures. Ends with an eye towards the practical, with "A Time-frequency search for stock market anomalies. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780817639181
  • Publisher: Birkhauser Verlag
  • Publication date: 12/18/1997
  • Series: Applied and Numerical Harmonic Analysis Series
  • Edition description: 1998
  • Edition number: 1
  • Pages: 284
  • Product dimensions: 0.69 (w) x 9.21 (h) x 6.14 (d)

Table of Contents

1 Review of algebra 1
2 Linear algebra and abelian groups 19
3 Fourier transform over A 25
4 Poisson summation formula 47
5 Zak transform 57
6 Weyl-Heisenberg systems 77
7 Zak transform and W-H systems 93
8 Algorithms for W-H systems 117
9 Orthogonal projection theorem 135
10 Cross-ambiguity function 141
11 Ambiguity surfaces 151
12 Orthonormal W-H systems 155
13 Duality 169
14 Frames 187
15 Implementation 199
16 Algebra of multirate structures 219
17 Multirate structures 239
18 A Time-frequency search for stock market anomalies 261
References 275
Index 281
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