Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Discrete Wavelets with Quaternion and Clifford Coefficients

Discrete Wavelets with Quaternion and Clifford Coefficients In this paper we use matrix representations of quaternions and Clifford algebras and solve the same matrix equations in each case to find Daubechies quaternion and Clifford scaling filters. We use paraunitary completion of the polyphase matrix to find corresponding quaternion and Clifford wavelet filters. We then use the cascade algorithm on our filters to find quaternion and Clifford scaling and wavelet functions, which we illustrate using all possible projections onto two and three dimensions: to our knowledge, this is the first time that this has been done. We discuss the shapes of these functions and conclude with a consideration of what we could actually do with our filters. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Applied Clifford Algebras Springer Journals

Discrete Wavelets with Quaternion and Clifford Coefficients

Fletcher, Peter
Advances in Applied Clifford Algebras , Volume 28 (3) – Jun 5, 2018
Download PDF
30 pages

Loading next page...
 
/lp/springer_journal/discrete-wavelets-with-quaternion-and-clifford-coefficients-28JCCpQLyu
Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Physics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Applications of Mathematics; Physics, general
ISSN
0188-7009
eISSN
1661-4909
DOI
10.1007/s00006-018-0876-5
Publisher site
See Article on Publisher Site

Abstract

In this paper we use matrix representations of quaternions and Clifford algebras and solve the same matrix equations in each case to find Daubechies quaternion and Clifford scaling filters. We use paraunitary completion of the polyphase matrix to find corresponding quaternion and Clifford wavelet filters. We then use the cascade algorithm on our filters to find quaternion and Clifford scaling and wavelet functions, which we illustrate using all possible projections onto two and three dimensions: to our knowledge, this is the first time that this has been done. We discuss the shapes of these functions and conclude with a consideration of what we could actually do with our filters.

Journal

Advances in Applied Clifford Algebras – Springer Journals

Published: Jun 5, 2018

References

  • Two-channel quadrature mirror filter bank: an overview
    Agrawal, SK; Sahu, OP
  • The theory and use of the quaternion wavelet transform
    Bayro-Corrochano, E
  • Orthonormal bases of compactly supported wavelets
    Daubechies, I
  • Matrix representations of quaternions
    Farebrother, RW; Groß, J; Troschke, S-O
  • The development of the quaternion wavelet transform
    Fletcher, P; Sangwine, SJ
  • An Introduction to Gröbner Bases
    Fröberg, R
  • Matrix-valued and quaternion wavelets
    Ginzberg, P; Walden, AT
  • Wavelets and Multiwavelets
    Keinert, F
  • Applications of complex valued wavelet transforms to subband decomposition
    Lawton, W
  • Clifford Algebras and Spinors. London Mathematical Society Lecture Note Series
    Lounesto, P
  • Multiresolution approximations and wavelet orthonormal bases of $${L}^2({\mathbb{R}})$$ L 2 ( R )
    Mallat, SG
  • Clifford multivector toolbox (for MATLAB)
    Sangwine, SJ; Hitzer, E
  • Wavelets and Filter Banks
    Strang, G; Nguyen, T
  • Wavelet analysis of matrix-valued time-series
    Walden, AT; Serroukh, A
  • Vector-valued wavelets and vector filter banks
    Xia, X-G; Suter, BW
  • Orthogonal complex filter banks and wavelets: some properties and design
    Zhang, X-P; Desai, MD; Peng, Y-N