Actions for Complex and hypercomplex analytic signals : theory and applications
Complex and hypercomplex analytic signals : theory and applications / Stefan L. Hahn, Kajetana M. Snopek
- Author
- Hahn, Stefan L.
- Published
- Boston : Artech House, [2017]
- Physical Description
- xii, 292 pages : illustrations (black and white) ; 24 cm.
- Additional Creators
- Snopek, Kajetana M.
- Series
- Contents
- Machine generated contents note: 1.1.Introduction -- 1.1.1.The Signal Domain Method -- 1.1.2.The Frequency Domain Method -- 1.2.A Historical Survey -- References -- 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 Algebras -- 2.4.Applications of Hypercomplex Algebras in Signal Processing -- 2.5.Summary -- References -- 3.1.The Notion of an Orthant -- 3.2.Single-Orthant Operators -- 3.3.Decomposition of Real Functions into Even and Odd Terms -- References -- 4.1.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 Components -- 4.2.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 2-D FT -- 4.3.2.Relation Between OFT and 3-D 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 -- 5.1.1-D Analytic Signals as Boundary Distributions of 1-D Analytic Functions -- 5.2.The n-D 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 n-D 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 -- 5.6.3.Selected Applications -- References -- 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.Ranking 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 -- 7.1.Introduction -- 7.2.Polar Representation of Complex Numbers -- 7.3.Polar Representation of 1-D Analytic Signals -- 7.3.1.Representation of the Instantaneous Complex Frequency using the Wigner Distribution -- 7.4.Polar Representation of 2-D Analytic Signals -- 7.4.1.2-D Complex Analytic Signals with Single-Quadrant Spectra -- 7.4.2.2-D Hypercomplex Quaternion Analytic Signals with Single-Quadrant Spectra -- 7.4.3.Relations between the Analytic and Quaternion 2-D Phase Functions -- 7.4.4.Polar Representation of the Monogenic 2-D Signal -- 7.4.5.Common Examples for 2-D Polar Representations of Analytic, Quaternion,and Monogenic Signals -- 7.5.Polar Representation of 3-D Analytic Signals -- 7.5.1.3-D Complex Signals with Single Octant Spectra -- 7.5.2.3-D Octonion Signals with Single Octant Spectra -- References -- 8.1.Definition of a Quasi-Analytic Signal -- 8.2.The 1-D Quasi-Analytic Signals -- 8.3.Phase Signals -- 8.4.The n-D Quasi-Analytic Signals -- References -- 9.1.Wigner Distributions and Woodward Ambiguity Functions of Complex Analytic Signals -- 9.1.1.WDs and AFs of 1-D Signals -- 9.1.2.WDs and AFs of 2-D Complex Signals -- 9.1.3.WDs and AFs of 2-D Complex Analytic Signals -- 9.2.Wigner Distributions and Woodward Ambiguity Functions of Quaternion and Monogenic Signals -- 9.2.1.The WDs of Quaternion Signals -- 9.2.2.AFs of Quaternion Signals -- 9.2.3.WDs of Monogenic Signals -- 9.2.4.AFs of Monogenic Signals -- 9.3.Double-Dimensional Wigner Distributions -- 9.4.Applications of Space-Frequency Distributions in Signal Processing -- 9.4.1.Wigner Distribution in Noise Analysis -- 9.4.2.Wigner Distribution in Image Processing -- References -- 10.1.Kramers-Kronig Relations -- 10.2.Extension of the Notion of Causality to Higher Dimensions -- 10.2.1.Derivation of the Dispersion Relations -- 10.3.Summary -- References -- References -- Selected Bibliography -- Selected Bibliography -- Selected Bibliography -- Selected Bibliography -- Selected Bibliography.
- Subject(s)
- ISBN
- 9781630811327 (hardback)
1630811327 (hardback) - Bibliography Note
- Includes bibliographical references and index.
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