Complex and hypercomplex analytic signals. Theory and applications
type: Item
instance of: scholarly article
zbMATH Open document ID: 1361.94002
author: Stefan L. Hahn
author: Kajetana M. Snopek
publication date: 2016-10-07T00:00:00Z
Mathematics Subject Classification ID: 94-02
Mathematics Subject Classification ID: 94A08
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 17A35
zbMATH DE Number: 6635643
zbMATH Keywords: signal processing
zbMATH Keywords: image processing
zbMATH Keywords: monograph
zbMATH Keywords: multidimensional hypercomplex signals
zbMATH Keywords: hypercomplex numbers
zbMATH Keywords: quaternions
zbMATH Keywords: octonions
zbMATH Keywords: hypercomplex Fourier transform
zbMATH Keywords: hypercomplex analytic signals
zbMATH Keywords: polar representation
zbMATH Keywords: space-frequency representation
MaRDI profile type: Publication
Recommended article: Hypercomplex signals-a novel extension of the analytic signal to the multidimensional case
Recommended article: The unified theory of \(n\)-dimensional complex and hypercomplex analytic signals
Recommended article: Spatiotemporal analysis of complex signals: Theory and applications
Recommended article: Higher-order spectral analysis of complex signals
Recommended article: An application of entire function theory to analytic signals
Recommended article: Complex signals with single-orthant spectra as boundary distributions of multidimensional analytic functions
Recommended article: Q4330319
Recommended article: Analytic signals and harmonic measures
Recommended article: Q3342338
title: Complex and hypercomplex analytic signals. Theory and applications
review text: With this interesting book, the authors present the first comprehensive publication on the theory of multidimensional complex and hypercomplex signals which is illustrated by numerous examples and practical applications in digital signal and image processing. This monograph is mainly based on the research of both authors over more than 20 years. Starting point was the theory of multidimensional analytic signals with single-orthant spectra introduced by \textit{S. L. Hahn} [``Multidimensional complex signals with single-orthant spectra'', Proc. IEEE 80, No. 8, 1287--1300 (1992; \url{doi:10.1109/5.158601})]. Further in the book of \textit{S. L. Hahn} [Hilbert transforms in signal processing. Boston, MA: Artech House (1996; Zbl 0910.94003)], one can find a description of the theory of multidimensional complex analytic signals.NEWLINENEWLINENEWLINEThe book under review is divided into 10 chapters, a summary, and 8 appendices. After an introductory chapter, chapter 2 gives an overview of algebras of hypercomplex numbers, namely of Caley-Dickson algebras of quaternions and octonions as well as of Clifford algebras of biquaternions and bioctonions. Orthants of a multidimensional Cartesian space and single-orthant operators are introduced in Chapter 3. In Chapter 4, the theory of complex and hypercomplex Fourier transforms of multidimensional signals is presented. Chapter 5 explains the theory of multidimensional complex and hypercomplex analytic signals. Chapter 6 is devoted to the ranking of complex and hypercomplex analytic signals. Chapter 7 presents polar representations of \(n\)-dimensional complex and hypercomplex analytic signals for \(n=1,\,2,\,3\). Quasi-analytic signals are handled in Chapter 8. Using Wigner distribution and corresponding Woodward's ambiguity function, space-frequency representations of \(n\)-dimensional complex and hypercomplex analytic signals for \(n=1\) and \(n=2\) are given in Chapter 9. In the last chapter, the causality of multidimensional…
reviewed by: Manfred Tasche
description: scientific article; zbMATH DE number 6635643