# Quaternion and Clifford Fourier Transforms and Wavelets

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Part of the Trends in Mathematics book series (TM)

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Part of the Trends in Mathematics book series (TM)

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.

complex numbers hypercomplex algebra and analysis image and signal processing matrix isomorphisms quaternionic spectral analysis

- DOI https://doi.org/10.1007/978-3-0348-0603-9
- Copyright Information Springer Basel 2013
- Publisher Name Birkhäuser, Basel
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-0348-0602-2
- Online ISBN 978-3-0348-0603-9
- Buy this book on publisher's site