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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

Advances in Applied Clifford Algebras , Volume 28 (3) – Jun 5, 2018

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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 AlgebrasSpringer Journals

Published: Jun 5, 2018

References