| Description |
1 online resource (231 pages) |
| Contents |
Cover -- Contents -- Preface -- 1. Introduction -- 1.1 Nomenclature -- 1.2 Main Abbreviations -- 1.3 Array of Sensors 8212; Environment -- 1.4 Pictorial Notation -- 1.4.1 Spaces/Subspaces -- 1.4.2 Projection Operator -- 1.5 Principal Symbols -- 1.6 Modelling the Array Signal-Vector and Array Manifold -- 1.7 Significance of Array Manifolds -- 1.8 An Outline of the Book -- 2. Differential Geometry of Array Manifold Curves -- 2.1 Manifold Curve Representation 8212; Basic Concepts -- 2.2 Curvatures and Coordinate Vectors in CN -- 2.2.1 Number of Curvatures and Symmetricity in Linear Arrays -- 2.2.2 8220;Moving Frame and Frame Matrix -- 2.2.3 Frame Matrix and Curvatures -- 2.2.4 Narrow and Wide Sense Orthogonality -- 2.3 8220;Hyperhelical Manifold Curves -- 2.3.1 Coordinate Vectors and Array Symmetricity -- 2.3.2 Evaluating the Curvatures of Uniform Linear Array Manifolds -- 2.4 The Manifold Length and Number of Windings (or Half Windings) -- 2.5 The Concept of 8220;Inclination of the Manifold -- 2.6 The Manifold-Radii Vector -- 2.7 Appendices -- 2.7.1 Proof of Eq. (2.24) -- 2.7.2 Proof of Theorem 2.1 -- 3. Differential Geometry of Array Manifold Surfaces -- 3.1 Manifold Metric -- 3.2 The First Fundamental Form -- 3.3 Christoffel Symbol Matrices -- 3.4 Intrinsic Geometry of a Surface -- 3.4.1 Gaussian Curvature -- 3.4.2 Curves on a Manifold Surface: Geodesic Curvature -- 3.4.3 Geodesic Curvature -- 3.5 The Concept of 8220;Development -- 3.6 Summary -- 3.7 Appendices -- 3.7.1 Proof of Eq. (3.36) 8212; Geodesic Curvature -- 4. Non-Linear Arrays: (, 966;)-Parametrization of Array Manifold Surfaces -- 4.1 Manifold Metric and Christoffel Symbols -- 4.2 3D-grid Arrays of Omnidirectional Sensors -- 4.3 Planar Arrays of Omnidirectional Sensors -- 4.4 Families of -- and 966;-curves on theManifold Surface -- 4.5 8220;Development of Non-linear Array Geometries -- 4.6 Summary -- 4.7 Appendices -- 4.7.1 Proof that the Gaussian Curvature of an Omni-directional Sensor Planar Array Manifold is Zero -- 4.7.2 Proof of the Expression of det G for Planar Arrays in Table 4.2 -- 4.7.3 Proof of 8220;Development Theorem 4.6 -- 5. Non-Linear Arrays: (945;, 946;)-Parametrization -- 5.1 Mapping from the (, 966;) Parameter Space to Cone-Angle Parameter Space -- 5.2 Manifold Vector in Terms of a Cone-Angle -- 5.3 Intrinsic Geometry of the Array Manifold Based on Cone-Angle Parametrization -- 5.4 Defining the Families of -- and -parameter Curves -- 5.5 Properties of 945;- and 946;-parameter Curves -- 5.5.1 Geodecity -- 5.5.2 Length of Parameter Curves -- 5.5.3 Shape of 945;- and 946;-curves -- 5.6 8220;Development of 945;- and 946;-parameter Curves -- 6. Array Ambiguities -- 6.1 Classification of Ambiguities -- 6.2 The Concept of an Ambiguous Generator Set -- 6.3 Partitioning the Array Manifold Curve into Segments of Equal Length -- 6.3.1 Calculation of Ambiguous Generator Sets of Linear (or ELA) Array Geometries -- 6.4 Representative Examples -- 6.5 Handling Ambiguities in Planar Arrays -- 6.5.1 Ambiguities on 966;-curves -- 6.5.2 Ambiguities on 945;-curves/946;-curves -- 6.5.3 Some Comments on Planar Arrays -- 6.5.4 Ambiguous Generator Lines -- 6.6 Ambiguities and Manifold Length -- 6.7 Appendices -- 6.7.1 Proof of T |
| Summary |
In view of the significance of the array manifold in array processingand array communications, the role of differential geometry as ananalytical tool cannot be overemphasized. Differential geometry ismainly confined to the investigation of the geometric properties ofmanifolds in three-dimensional Euclidean space R3 and inreal spaces of higher dimension |
| Bibliography |
Includes bibliographical references (p. 215-218) and index |
| Notes |
English |
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Print version record |
| Subject |
Array processors.
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Geometry, Differential.
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Array processors
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Geometry, Differential
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Engineering & Applied Sciences.
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Computer Science.
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| Form |
Electronic book
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| ISBN |
9781860946028 |
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186094602X |
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1281866601 |
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9781281866608 |
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1860944221 |
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9781860944222 |
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9786611866600 |
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6611866604 |
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