Author 
Hahn, Stefan L.,

Series 
Artech House signal processing Library 

Artech House signal processing library.

Subject 
Signal processing.


Functions of complex variables.

Alt Name 
Snopek, Kajetana M.,

Description 
1 online resource : illustrations 
Note 
Print version record. 
Bibliography Note 
Includes bibliographical references and index. 
Contents 
Complex and Hypercomplex Analytic Signals: Theory and Applications; Preface; Contents; 1 Introduction and Historical Background; 1.1 Introduction; 1.1.1 The Signal Domain Method; 1.1.2 The Frequency Domain Method; 1.2 A Historical Survey; References; 2 Survey of Chosen Hypercomplex Algebras; 2.1 CayleyDickson Algebras; 2.1.1 The CayleyDickson Construction; 2.1.2 The CayleyDickson algebra of quaternions; 2.1.3 The CayleyDickson Algebra of Octonions; 2.2 Selected Clifford Algebras; 2.2.1 The Clifford Algebra of Biquaternions; 2.2.2 The Clifford Algebra of Bioctonions. 

2.3 Comparison of Algebras2.4 Applications of Hypercomplex Algebras in Signal Processing; 2.5 Summary; References; 3 Orthants of the nDimensional Cartesian Space and SingleOrthant Operators; 3.1 The Notion of an Orthant; 3.2 SingleOrthant Operators; 3.3 Decomposition of Real Functions into Even and Odd Terms; References; 4 Fourier Transformation in Analysis of nDimensional Signals; 4.1 Complex nD Fourier Transformation; 4.1.1 Spectrum of a 1D Real Signal in Terms of its Even and Odd Components; 4.1.2 Spectrum of a 2D Real Signal in Terms of its Even and Odd Components. 

4.1.3 Spectrum of a 3D Real Signal in Terms of its Even and Odd Components4.2 CayleyDickson Fourier Transformation; 4.2.1 General Formulas; 4.2.2 Quaternion Fourier Spectrum in Terms of its Even and Odd Components; 4.2.3 Octonion Fourier Spectrum in Terms of its Even and Odd Components; 4.3 Relations Between Complex and Hypercomplex Fourier Transforms; 4.3.1 Relation Between QFT and 2D FT; 4.3.2 Relation Between OFT and 3D FT; 4.4 Survey of Applications of Complex and Hypercomplex Fourier Transformations; 4.4.1 Applications in the Domain of Analytic Signals; 4.5 Summary; References. 

5 Complex and Hypercomplex Analytic Signals5.1 1D Analytic Signals as Boundary Distributions of 1D Analytic Functions; 5.2 The nD Analytic Signal; 5.2.1 The 2D Complex Analytic Signals; 5.2.2 3D Complex Analytic Signals; 5.3 Hypercomplex nD Analytic Signals; 5.3.1 2D Quaternion Signals; 5.3.2 3D Hypercomplex Analytic Signals; 5.4 Monogenic 2D Signals; 5.5 A Short Survey of the Notions of Analytic Signals with Single Orthant Spectra; 5.6 Survey of Application of nD Analytic Signals; 5.6.1 Applications Presented in Other Chapters of this Book. 

5.6.2 Applications Described in Hahn's Book on Hilbert Transforms [7]5.6.3 Selected Applications; References; 6 Ranking of Analytic Signals; 6.1 Definition of a Suborthant; 6.1.1 Subquadrants in 2D; 6.1.2 Suboctants in 3D; 6.2 Ranking of Complex Analytic Signals; 6.2.1 Ranking of 2D Complex Analytic Signals; 6.2.2 Ranking of 3D Complex Analytic Signals; 6.3 Sanking of Hypercomplex Analytic Signals; 6.3.1 Ranking of 2D CayleyDickson Analytic Signals; 6.3.2 Ranking of 3D CayleyDickson Analytic Signals; 6.4 Summary; References; 7 Polar Representation of Analytic Signals; 7.1 Introduction. 
Note 
7.2 Polar Representation of Complex Numbers. 
Summary 
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 indepth 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 ndimensional Cartesian space and singleorthant operators are explored. This book also covers topics including, the polar representation of analytic signals, quasianalytic signals, the spacefrequency of nD complex and hypercomplex signals as well as the causality of signals. 
ISBN 
9781630814380 (electronic bk.) 

1630814385 (electronic bk.) 

9781630811334 

1630811335 

9781630811327 

1630811327 
OCLC # 
986441993 
Additional Format 
Print version: Hahn, Stefan L. Complex and hypercomplex analytic signals. Boston : Artech House, [2017] 9781630811327 (DLC) 2017288105 (OCoLC)968791243 
