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Quaternion and Clifford Fourier Transforms and Wavelets

Hitzer, E and Sangwine, SJ (2013) 'Quaternion and Clifford Fourier Transforms and Wavelets.' Quaternion and Clifford Fourier Transforms and Wavelets, abs/13. pp. 1-338. ISSN 2297-0215


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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.

Item Type: Article
Additional Information: 25 pages, 5 figures
Uncontrolled Keywords: Quaternion signals; orthogonal 2D planes split; quaternion Fourier transformations; steerable transforms; geometric interpretation; fast implementations
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Faculty of Science and Health
Faculty of Science and Health > Computer Science and Electronic Engineering, School of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 04 Dec 2014 11:27
Last Modified: 15 Jan 2022 00:38

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