An Introduction to Finite Tight Frames

  • Shayne F. D. Waldron

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

Table of contents

  1. Front Matter
    Pages i-xx
  2. Shayne F. D. Waldron
    Pages 1-5
  3. Shayne F. D. Waldron
    Pages 7-29
  4. Shayne F. D. Waldron
    Pages 31-69
  5. Shayne F. D. Waldron
    Pages 99-111
  6. Shayne F. D. Waldron
    Pages 113-149
  7. Shayne F. D. Waldron
    Pages 151-163
  8. Shayne F. D. Waldron
    Pages 165-187
  9. Shayne F. D. Waldron
    Pages 189-207
  10. Shayne F. D. Waldron
    Pages 209-243
  11. Shayne F. D. Waldron
    Pages 245-264
  12. Shayne F. D. Waldron
    Pages 265-330
  13. Shayne F. D. Waldron
    Pages 331-359
  14. Shayne F. D. Waldron
    Pages 361-427
  15. Shayne F. D. Waldron
    Pages 429-439
  16. Shayne F. D. Waldron
    Pages 441-470
  17. Back Matter
    Pages 471-587

About this book


This textbook is an introduction to the theory and applications of finite tight frames, an area that has developed rapidly in the last decade. Stimulating much of this growth are the applications of finite frames to diverse fields such as signal processing, quantum information theory, multivariate orthogonal polynomials, and remote sensing.

Key features and topics:

* First book entirely devoted to finite frames

* Extensive exercises and MATLAB examples for classroom use

* Important examples, such as harmonic and Heisenberg frames, are presented in preliminary chapters, encouraging readers to explore and develop an intuitive feeling for tight frames

* Later chapters delve into general theory details and recent research results

* Many illustrations showing the special aspects of the geometry of finite frames

* Provides an overview of the field of finite tight frames

* Discusses future research directions in the field

Featuring exercises and MATLAB examples in each chapter, the book is well suited as a textbook for a graduate course or seminar involving finite frames. The self-contained, user-friendly presentation also makes the work useful as a self-study resource or reference for graduate students, instructors, researchers, and practitioners in pure and applied mathematics, engineering, mathematical physics, and signal processing.


Heisenberg frames MATLAB finite tight frames harmonic frames multivariate orthogonal polynomials quantum information theory remote sensing signal processing tight frames

Authors and affiliations

  • Shayne F. D. Waldron
    • 1
  1. 1.Department of MathematicsUniversity of AucklandAucklandNew Zealand

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media, LLC 2018
  • Publisher Name Birkhäuser, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4814-5
  • Online ISBN 978-0-8176-4815-2
  • Series Print ISSN 2296-5009
  • Series Online ISSN 2296-5017
  • Buy this book on publisher's site