Quaternion and Clifford Fourier Transforms and Wavelets

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.

Quaternion and Clifford Fourier Transforms and Wavelets

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.

More Books:

Quaternion and Clifford Fourier Transforms and Wavelets
Language: en
Pages: 338
Authors: Eckhard Hitzer, Stephen J. Sangwine
Categories: Mathematics
Type: BOOK - Published: 2013-06-24 - Publisher: Springer Science & Business Media

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
Quaternion and Clifford Fourier Transforms
Language: en
Pages: 474
Authors: Eckhard Hitzer
Categories: Mathematics
Type: BOOK - Published: 2021-09-21 - Publisher: CRC Press

Quaternion and Clifford Fourier Transforms describes the development of quaternion and Clifford Fourier transforms in Clifford (geometric) algebra over the last 30 years. It is the first comprehensive, self-contained book covering this vibrant new area of pure and applied mathematics in depth. The book begins with a historic overview, followed
Quaternion Fourier Transforms for Signal and Image Processing
Language: en
Pages: 160
Authors: Todd A. Ell, Nicolas Le Bihan, Stephen J. Sangwine
Categories: Technology & Engineering
Type: BOOK - Published: 2014-06-23 - Publisher: John Wiley & Sons

Based on updates to signal and image processing technology made in the last two decades, this text examines the most recent research results pertaining to Quaternion Fourier Transforms. QFT is a central component of processing color images and complex valued signals. The book’s attention to mathematical concepts, imaging applications, and
Towards Intelligent Systems Modeling and Simulation
Language: en
Pages: 435
Authors: Samsul Ariffin Abdul Karim, Afza Shafie
Categories: Technology & Engineering
Type: BOOK - Published: 2021-10-19 - Publisher: Springer Nature

This book creates the emergence of disruptive technologies that have led to a significant change in the role of mathematics and statistics for problem solving, with the use of sophisticated software and hardware in solving complex systems and process. In the era of digital technology, mathematics and statistics need to
Geometric Science of Information
Language: en
Pages: 879
Authors: Frank Nielsen, Frédéric Barbaresco
Categories: Computers
Type: BOOK - Published: 2013-08-19 - Publisher: Springer

This book constitutes the refereed proceedings of the First International Conference on Geometric Science of Information, GSI 2013, held in Paris, France, in August 2013. The nearly 100 papers presented were carefully reviewed and selected from numerous submissions and are organized into the following thematic sessions: Geometric Statistics on Manifolds