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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 Algebras – Springer Journals
Published: Jun 5, 2018