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Complex and Hypercomplex Analytic Signals

Complex and Hypercomplex Analytic Signals
Author: Stefan L. Hahn
Publisher: Artech House
Total Pages: 307
Release: 2016-12
Genre: Technology & Engineering
ISBN: 1630814385
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Based on the bestselling Artech House classic title, Hilbert Transforms Signal Processing, this comprehensive new resource introduces complex and hypercomplex analytic signals and their applications. Professionals find in-depth explanations of the theory of multidimensional complex and hypercomplex signals illustrated with numerous examples and followed by practical applications. The survey of chosen hypercomplex algebras and the orthants of the n-dimensional Cartesian space and single-orthant operators are explored. This book also covers topics including, the polar representation of analytic signals, quasi-analytic signals, the space-frequency of n-D complex and hypercomplex signals as well as the causality of signals.

Linear Systems, Signal Processing and Hypercomplex Analysis

Linear Systems, Signal Processing and Hypercomplex Analysis
Author: Daniel Alpay
Publisher: Springer
Total Pages: 316
Release: 2019-08-08
Genre: Mathematics
ISBN: 3030184846
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This volume includes contributions originating from a conference held at Chapman University during November 14-19, 2017. It presents original research by experts in signal processing, linear systems, operator theory, complex and hypercomplex analysis and related topics.

Quaternionic Integral Transforms

Quaternionic Integral Transforms
Author: Eckhard Hitzer
Publisher: Springer Nature
Total Pages: 187
Release: 2023-09-09
Genre: Mathematics
ISBN: 3031283759
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This book presents a machine-generated literature overview of quaternion integral transforms from select papers published by Springer Nature, which have been organized and introduced by the book’s editor. Each chapter presents summaries of predefined themes and provides the reader with a basis for further exploration of the topic. As one of the experimental projects initiated by Springer Nature for AI book content generation, this book shows the latest developments in the field. It will be a useful reference for students and researchers who are interested in exploring the latest developments in quaternion integral transforms.

Quaternion and Clifford Fourier Transforms and Wavelets

Quaternion and Clifford Fourier Transforms and Wavelets
Author: Eckhard Hitzer
Publisher: Springer Science & Business Media
Total Pages: 358
Release: 2013-06-24
Genre: Mathematics
ISBN: 3034806035
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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.

Hypercomplex Analysis: New Perspectives and Applications

Hypercomplex Analysis: New Perspectives and Applications
Author: Swanhild Bernstein
Publisher: Springer
Total Pages: 228
Release: 2014-10-10
Genre: Mathematics
ISBN: 3319087711
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Hypercomplex analysis is the extension of complex analysis to higher dimensions where the concept of a holomorphic function is substituted by the concept of a monogenic function. In recent decades this theory has come to the forefront of higher dimensional analysis. There are several approaches to this: quaternionic analysis which merely uses quaternions, Clifford analysis which relies on Clifford algebras, and generalizations of complex variables to higher dimensions such as split-complex variables. This book includes a selection of papers presented at the session on quaternionic and hypercomplex analysis at the ISAAC conference 2013 in Krakow, Poland. The topics covered represent new perspectives and current trends in hypercomplex analysis and applications to mathematical physics, image analysis and processing, and mechanics.

Empowering Novel Geometric Algebra for Graphics and Engineering

Empowering Novel Geometric Algebra for Graphics and Engineering
Author: Eckhard Hitzer
Publisher: Springer Nature
Total Pages: 138
Release: 2023-04-26
Genre: Mathematics
ISBN: 3031309235
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This book constitutes the proceedings of the Workshop Empowering Novel Geometric Algebra for Graphics and Engineering, ENGAGE 2022, held in conjunction with Computer Graphics International conference, CGI 2022, which took place virtually, in September 2022. The 10 full papers included in this volume were carefully reviewed and selected from 12 submissions. The workshop focused specifically on important aspects of geometric algebra including algebraic foundations, digitized transformations, orientation, conic fitting, protein modelling, digital twinning, and multidimensional signal processing.

Signal Digitization and Reconstruction in Digital Radios

Signal Digitization and Reconstruction in Digital Radios
Author: Yefim Poberezhskiy
Publisher: Artech House
Total Pages: 340
Release: 2018-12-31
Genre: Technology & Engineering
ISBN: 1630814016
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This comprehensive resource provides the latest information on digitization and reconstruction (D&R) of analog signals in digital radios. Readers learn how to conduct comprehensive analysis, concisely describe the major signal processing procedures carried out in the radios, and demonstrate the dependence of these procedures on the quality of D&R. The book presents and analyzes the most promising and theoretically sound ways to improve the characteristics of D&R circuits and illustrate the influence of these improvements on the capabilities of digital radios. The book is intended to bridge the gap that exists between theorists and practical engineers developing D&R techniques by introducing new signal transmission and reception methods that can effectively utilize the unique capabilities offered by novel digitization and reconstruction techniques.

Progress in Industrial Mathematics at ECMI 2018

Progress in Industrial Mathematics at ECMI 2018
Author: István Faragó
Publisher: Springer Nature
Total Pages: 605
Release: 2019-11-22
Genre: Science
ISBN: 3030275507
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This book explores mathematics in a wide variety of applications, ranging from problems in electronics, energy and the environment, to mechanics and mechatronics. The book gathers 81 contributions submitted to the 20th European Conference on Mathematics for Industry, ECMI 2018, which was held in Budapest, Hungary in June 2018. The application areas include: Applied Physics, Biology and Medicine, Cybersecurity, Data Science, Economics, Finance and Insurance, Energy, Production Systems, Social Challenges, and Vehicles and Transportation. In turn, the mathematical technologies discussed include: Combinatorial Optimization, Cooperative Games, Delay Differential Equations, Finite Elements, Hamilton-Jacobi Equations, Impulsive Control, Information Theory and Statistics, Inverse Problems, Machine Learning, Point Processes, Reaction-Diffusion Equations, Risk Processes, Scheduling Theory, Semidefinite Programming, Stochastic Approximation, Spatial Processes, System Identification, and Wavelets. The goal of the European Consortium for Mathematics in Industry (ECMI) conference series is to promote interaction between academia and industry, leading to innovations in both fields. These events have attracted leading experts from business, science and academia, and have promoted the application of novel mathematical technologies to industry. They have also encouraged industrial sectors to share challenging problems where mathematicians can provide fresh insights and perspectives. Lastly, the ECMI conferences are one of the main forums in which significant advances in industrial mathematics are presented, bringing together prominent figures from business, science and academia to promote the use of innovative mathematics in industry.