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Time-Frequency Representations

  • Richard Tolimieri
  • Myoung An

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Richard Tolimieri, Myoung An
    Pages 1-18
  3. Richard Tolimieri, Myoung An
    Pages 19-24
  4. Richard Tolimieri, Myoung An
    Pages 25-46
  5. Richard Tolimieri, Myoung An
    Pages 47-56
  6. Richard Tolimieri, Myoung An
    Pages 57-75
  7. Richard Tolimieri, Myoung An
    Pages 77-92
  8. Richard Tolimieri, Myoung An
    Pages 93-116
  9. Richard Tolimieri, Myoung An
    Pages 117-133
  10. Richard Tolimieri, Myoung An
    Pages 135-139
  11. Richard Tolimieri, Myoung An
    Pages 141-150
  12. Richard Tolimieri, Myoung An
    Pages 151-153
  13. Richard Tolimieri, Myoung An
    Pages 155-168
  14. Richard Tolimieri, Myoung An
    Pages 169-185
  15. Richard Tolimieri, Myoung An
    Pages 187-197
  16. Richard Tolimieri, Myoung An
    Pages 199-218
  17. Richard Tolimieri, Myoung An
    Pages 219-238
  18. Richard Tolimieri, Myoung An
    Pages 239-259
  19. Sudeshna Adak, Abhinanda Sarkar
    Pages 261-273
  20. Back Matter
    Pages 275-284

About this book

Introduction

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.

Keywords

Expander Fourier analysis Fourier transform Frequency Mathematics algebra algorithms

Authors and affiliations

  • Richard Tolimieri
    • 1
  • Myoung An
    • 2
  1. 1.Department of Electrical EngineeringCity College of New YorkNew YorkUSA
  2. 2.A. J. Devaney AssociatesBostonUSA

Bibliographic information