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Complex and hypercomplex analytic signals : theory and applications / / Stefan L. Hahn, Kajetana M. Snopek
| Complex and hypercomplex analytic signals : theory and applications / / Stefan L. Hahn, Kajetana M. Snopek |
| Autore | Hahn Stefan L. |
| Pubbl/distr/stampa | Norwood, Massachusetts : , : Artech House, , [2017] |
| Descrizione fisica | 1 online resource (294 pages) : illustrations |
| Disciplina | 621.38223 |
| Collana | Artech House signal processing Library |
| Soggetto topico |
Signal processing
Functions of complex variables |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-63081-438-5 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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. |
| Record Nr. | UNINA-9910466027403321 |
Hahn Stefan L.
|
||
| Norwood, Massachusetts : , : Artech House, , [2017] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Complex and hypercomplex analytic signals : theory and applications / / Stefan L. Hahn, Kajetana M. Snopek
| Complex and hypercomplex analytic signals : theory and applications / / Stefan L. Hahn, Kajetana M. Snopek |
| Autore | Hahn Stefan L. |
| Pubbl/distr/stampa | Norwood, Massachusetts : , : Artech House, , [2017] |
| Descrizione fisica | 1 online resource (294 pages) : illustrations |
| Disciplina | 621.38223 |
| Collana | Artech House signal processing Library |
| Soggetto topico |
Signal processing
Functions of complex variables |
| ISBN | 1-63081-438-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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. |
| Record Nr. | UNINA-9910792712403321 |
|
Hahn Stefan L.
|
||
| Norwood, Massachusetts : , : Artech House, , [2017] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Complex and hypercomplex analytic signals : theory and applications / / Stefan L. Hahn, Kajetana M. Snopek
| Complex and hypercomplex analytic signals : theory and applications / / Stefan L. Hahn, Kajetana M. Snopek |
| Autore | Hahn Stefan L. |
| Pubbl/distr/stampa | Norwood, Massachusetts : , : Artech House, , [2017] |
| Descrizione fisica | 1 online resource (294 pages) : illustrations |
| Disciplina | 621.38223 |
| Collana | Artech House signal processing Library |
| Soggetto topico |
Signal processing
Functions of complex variables |
| ISBN | 1-63081-438-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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. |
| Record Nr. | UNINA-9910824824103321 |
|
Hahn Stefan L.
|
||
| Norwood, Massachusetts : , : Artech House, , [2017] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||