Trends in Mathematics

Quaternion and Clifford Fourier Transforms and Wavelets

Editors: Hitzer, Eckhard, Sangwine, Stephen J. (Eds.)

  • First book on this topics combining theory and applications
  • Comprehensive overview addressing both mathematicians and engineers
  • Provides a representative overview of the relevant literature
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eBook $129.00
price for USA (gross)
  • ISBN 978-3-0348-0603-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA
  • ISBN 978-3-0348-0602-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.00
price for USA
  • ISBN 978-3-0348-0777-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. This edited volume presents the state of the art in these hypercomplex transformations. The Clifford algebras unify Hamilton’s quaternions with Grassmann algebra. A Clifford algebra is a complete algebra of a vector space and all its subspaces including the measurement of volumes and dihedral angles between any pair of subspaces. Quaternion and Clifford algebras permit the systematic generalization of many known concepts.
 
This book provides comprehensive insights into current developments and applications including their performance and evaluation. Mathematically, it indicates where further investigation is required. For instance, attention is drawn to the matrix isomorphisms for hypercomplex algebras, which will help readers to see that software implementations are within our grasp.
 
It also contributes to a growing unification of ideas and notation across the expanding field of hypercomplex transforms and wavelets. The first chapter provides a historical background and an overview of the relevant literature, and shows how the contributions that follow relate to each other and to prior work. The book will be a valuable resource for graduate students as well as for scientists and engineers.

Table of contents (16 chapters)

  • Quaternion Fourier Transform: Re-tooling Image and Signal Processing Analysis

    Ell, Todd Anthony

    Pages 3-14

  • The Orthogonal 2D Planes Split of Quaternions and Steerable Quaternion Fourier Transformations

    Hitzer, Eckhard (et al.)

    Pages 15-39

  • Quaternionic Spectral Analysis of Non-Stationary Improper Complex Signals

    Bihan, Nicolas Le (et al.)

    Pages 41-56

  • Quaternionic Local Phase for Low-level Image Processing Using Atomic Functions

    Moya-Sánchez, E. Ulises (et al.)

    Pages 57-83

  • Bochner’s Theorems in the Framework of Quaternion Analysis

    Georgiev, S. (et al.)

    Pages 85-104

Buy this book

eBook $129.00
price for USA (gross)
  • ISBN 978-3-0348-0603-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA
  • ISBN 978-3-0348-0602-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.00
price for USA
  • ISBN 978-3-0348-0777-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Quaternion and Clifford Fourier Transforms and Wavelets
Editors
  • Eckhard Hitzer
  • Stephen J. Sangwine
Series Title
Trends in Mathematics
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0603-9
DOI
10.1007/978-3-0348-0603-9
Hardcover ISBN
978-3-0348-0602-2
Softcover ISBN
978-3-0348-0777-7
Series ISSN
2297-0215
Edition Number
1
Number of Pages
XXVII, 338
Topics