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Complex and hypercomplex analytic signals : theory and applications /
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...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Norwood, MA :
Artech House,
[2017]
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| Colección: | Artech House signal processing library.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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 Cayley-Dickson Algebras; 2.1.1 The Cayley-Dickson Construction; 2.1.2 The Cayley-Dickson algebra of quaternions; 2.1.3 The Cayley-Dickson 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 n-Dimensional Cartesian Space and Single-Orthant Operators; 3.1 The Notion of an Orthant; 3.2 Single-Orthant Operators; 3.3 Decomposition of Real Functions into Even and Odd Terms; References; 4 Fourier Transformation in Analysis of n-Dimensional Signals; 4.1 Complex n-D Fourier Transformation; 4.1.1 Spectrum of a 1-D Real Signal in Terms of its Even and Odd Components; 4.1.2 Spectrum of a 2-D Real Signal in Terms of its Even and Odd Components.
- 4.1.3 Spectrum of a 3-D Real Signal in Terms of its Even and Odd Components4.2 Cayley-Dickson 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 1-D Analytic Signals as Boundary Distributions of 1-D Analytic Functions; 5.2 The nD Analytic Signal; 5.2.1 The 2-D Complex Analytic Signals; 5.2.2 3-D Complex Analytic Signals; 5.3 Hypercomplex n-D Analytic Signals; 5.3.1 2-D Quaternion Signals; 5.3.2 3-D Hypercomplex Analytic Signals; 5.4 Monogenic 2-D 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 2-D; 6.1.2 Suboctants in 3-D; 6.2 Ranking of Complex Analytic Signals; 6.2.1 Ranking of 2-D Complex Analytic Signals; 6.2.2 Ranking of 3-D Complex Analytic Signals; 6.3 Sanking of Hypercomplex Analytic Signals; 6.3.1 Ranking of 2-D Cayley-Dickson Analytic Signals; 6.3.2 Ranking of 3-D Cayley-Dickson Analytic Signals; 6.4 Summary; References; 7 Polar Representation of Analytic Signals; 7.1 Introduction.