{"product_id":"sound-visualization-and-manipulation-9781118368473","title":"Sound Visualization and Manipulation","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eUnique in addressing two different problems     sound visualization and manipulation     in a unified way    Advances in signal processing technology are enabling ever more accurate visualization of existing sound fields and precisely defined sound field production.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eAbout the Author xi  \u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eAcknowledgments xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I ESSENCE OF ACOUSTICS\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Acoustic Wave Equation and Its Basic Physical Measures 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 3\u003c\/p\u003e \u003cp\u003e1.2 One-Dimensional Acoustic Wave Equation 3\u003c\/p\u003e \u003cp\u003e1.2.1 Impedance 9\u003c\/p\u003e \u003cp\u003e1.3 Three-Dimensional Wave Equation 10\u003c\/p\u003e \u003cp\u003e1.4 Acoustic Intensity and Energy 11\u003c\/p\u003e \u003cp\u003e1.4.1 Complex-Valued Pressure and Intensity 16\u003c\/p\u003e \u003cp\u003e1.5 The Units of Sound 18\u003c\/p\u003e \u003cp\u003e1.6 Analysis Methods of Linear Acoustic Wave Equation 27\u003c\/p\u003e \u003cp\u003e1.6.1 Acoustic Wave Equation and Boundary Condition 28\u003c\/p\u003e \u003cp\u003e1.6.2 Eigenfunctions and Modal Expansion Theory 31\u003c\/p\u003e \u003cp\u003e1.6.3 Integral Approach Using Green’s Function 35\u003c\/p\u003e \u003cp\u003e1.7 Solutions of the Wave Equation 39\u003c\/p\u003e \u003cp\u003e1.7.1 Plane Wave 40\u003c\/p\u003e \u003cp\u003e1.7.2 Spherical Wave 41\u003c\/p\u003e \u003cp\u003e1.8 Chapter Summary 46\u003c\/p\u003e \u003cp\u003eReferences 46\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Radiation, Scattering, and Diffraction 49\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction\/Study Objectives 49\u003c\/p\u003e \u003cp\u003e2.2 Radiation of a Breathing Sphere and a Trembling Sphere 50\u003c\/p\u003e \u003cp\u003e2.3 Radiation from a Baffled Piston 58\u003c\/p\u003e \u003cp\u003e2.4 Radiation from a Finite Vibrating Plate 65\u003c\/p\u003e \u003cp\u003e2.5 Diffraction and Scattering 70\u003c\/p\u003e \u003cp\u003e2.6 Chapter Summary 79\u003c\/p\u003e \u003cp\u003e2.7 Essentials of Radiation, Scattering, and Diffraction 80\u003c\/p\u003e \u003cp\u003e2.7.1 Radiated Sound Field from an Infinitely Baffled Circular Piston 80\u003c\/p\u003e \u003cp\u003e2.7.2 Sound Field at an Arbitrary Position Radiated by an Infinitely Baffled Circular Piston 81\u003c\/p\u003e \u003cp\u003e2.7.3 Understanding Radiation, Scattering, and Diffraction Using the Kirchhoff–Helmholtz Integral Equation 82\u003c\/p\u003e \u003cp\u003e2.7.4 Scattered Sound Field Using the Rayleigh Integral Equation 96\u003c\/p\u003e \u003cp\u003eReferences 97\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II SOUND VISUALIZATION\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Acoustic Holography 103\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 103\u003c\/p\u003e \u003cp\u003e3.2 The Methodology of Acoustic Source Identification 103\u003c\/p\u003e \u003cp\u003e3.3 Acoustic Holography: Measurement, Prediction, and Analysis 106\u003c\/p\u003e \u003cp\u003e3.3.1 Introduction and Problem Definitions 106\u003c\/p\u003e \u003cp\u003e3.3.2 Prediction Process 107\u003c\/p\u003e \u003cp\u003e3.3.3 Mathematical Derivations of Three Acoustic Holography Methods and Their Discrete Forms 113\u003c\/p\u003e \u003cp\u003e3.3.4 Measurement 119\u003c\/p\u003e \u003cp\u003e3.3.5 Analysis of Acoustic Holography 124\u003c\/p\u003e \u003cp\u003e3.4 Summary 129\u003c\/p\u003e \u003cp\u003eReferences 130\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Beamforming 137\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 137\u003c\/p\u003e \u003cp\u003e4.2 Problem Statement 138\u003c\/p\u003e \u003cp\u003e4.3 Model-Based Beamforming 140\u003c\/p\u003e \u003cp\u003e4.3.1 Plane and Spherical Wave Beamforming 140\u003c\/p\u003e \u003cp\u003e4.3.2 The Array Configuration 142\u003c\/p\u003e \u003cp\u003e4.4 Signal-Based Beamforming 145\u003c\/p\u003e \u003cp\u003e4.4.1 Construction of Correlation Matrix in Time Domain 146\u003c\/p\u003e \u003cp\u003e4.4.2 Construction of Correlation Matrix in Frequency Domain 151\u003c\/p\u003e \u003cp\u003e4.4.3 Correlation Matrix of Multiple Sound Sources 152\u003c\/p\u003e \u003cp\u003e4.5 Correlation-Based Scan Vector Design 160\u003c\/p\u003e \u003cp\u003e4.5.1 Minimum Variance Beamformer 160\u003c\/p\u003e \u003cp\u003e4.5.2 Linear Prediction 164\u003c\/p\u003e \u003cp\u003e4.6 Subspace-Based Approaches 170\u003c\/p\u003e \u003cp\u003e4.6.1 Basic Principles 170\u003c\/p\u003e \u003cp\u003e4.6.2 MUSIC Beamformer 173\u003c\/p\u003e \u003cp\u003e4.6.3 ESPRIT 180\u003c\/p\u003e \u003cp\u003e4.7 Wideband Processing Technique 182\u003c\/p\u003e \u003cp\u003e4.7.1 Frequency-Domain Approach: Mapping to the Beam Space 182\u003c\/p\u003e \u003cp\u003e4.7.2 Coherent Subspace Method (CSM) 184\u003c\/p\u003e \u003cp\u003e4.7.3 Partial Field Decomposition in Beam Space 185\u003c\/p\u003e \u003cp\u003e4.7.4 Time-Domain Technique 190\u003c\/p\u003e \u003cp\u003e4.7.5 Moving-Source Localization 198\u003c\/p\u003e \u003cp\u003e4.8 Post-Processing Techniques 204\u003c\/p\u003e \u003cp\u003e4.8.1 Deconvolution and Beamforming 204\u003c\/p\u003e \u003cp\u003e4.8.2 Nonnegativity Constraint 207\u003c\/p\u003e \u003cp\u003e4.8.3 Nonnegative Least-Squares Algorithm 209\u003c\/p\u003e \u003cp\u003e4.8.4 DAMAS 210\u003c\/p\u003e \u003cp\u003eReferences 212\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III SOUND MANIPULATION\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Sound Focusing 219\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 219\u003c\/p\u003e \u003cp\u003e5.2 Descriptions of the Problem of Sound Focusing 221\u003c\/p\u003e \u003cp\u003e5.2.1 Free-Field Radiation from Loudspeaker Arrays 221\u003c\/p\u003e \u003cp\u003e5.2.2 Descriptions of a Sound Field Depending on the Distance from the Array 221\u003c\/p\u003e \u003cp\u003e5.2.3 Fresnel Approximation 223\u003c\/p\u003e \u003cp\u003e5.2.4 Farfield Description of the Rayleigh Integral (Fraunhofer Approximation) 225\u003c\/p\u003e \u003cp\u003e5.2.5 Descriptors of Directivity 227\u003c\/p\u003e \u003cp\u003e5.3 Summing Operator (+) 230\u003c\/p\u003e \u003cp\u003e5.3.1 Delay-and-Sum Technique 230\u003c\/p\u003e \u003cp\u003e5.3.2 Beam Shaping and Steering 231\u003c\/p\u003e \u003cp\u003e5.3.3 Wavenumber Cone and Diffraction Limit 233\u003c\/p\u003e \u003cp\u003e5.3.4 Frequency Invariant Radiation Pattern 236\u003c\/p\u003e \u003cp\u003e5.3.5 Discrete Array and Grating Lobes 237\u003c\/p\u003e \u003cp\u003e5.4 Product Theorem (×) 240\u003c\/p\u003e \u003cp\u003e5.4.1 Convolution and Multiplication of Sound Beams 240\u003c\/p\u003e \u003cp\u003e5.4.2 On-Axis Pressure Response 243\u003c\/p\u003e \u003cp\u003e5.5 Differential Operator and Super-Directivity (−) 245\u003c\/p\u003e \u003cp\u003e5.5.1 Endfire Differential Patterns 245\u003c\/p\u003e \u003cp\u003e5.5.2 Combination of Delay-and-Sum and Endfire Differential Patterns 252\u003c\/p\u003e \u003cp\u003e5.5.3 Broadside Differential Pattern 252\u003c\/p\u003e \u003cp\u003e5.5.4 Combination of the Delay-and-Sum and Broadside Differential Patterns 258\u003c\/p\u003e \u003cp\u003e5.6 Optimization with Energy Ratios (÷) 259\u003c\/p\u003e \u003cp\u003e5.6.1 Problem Statement 259\u003c\/p\u003e \u003cp\u003e5.6.2 Capon’s Minimum Variance Estimator (Minimum Variance Beamformer) 261\u003c\/p\u003e \u003cp\u003e5.6.3 Acoustic Brightness and Contrast Control 262\u003c\/p\u003e \u003cp\u003e5.6.4 Further Analysis of Acoustic Brightness and Contrast Control 273\u003c\/p\u003e \u003cp\u003e5.6.5 Application Examples 276\u003c\/p\u003e \u003cp\u003eReferences 280\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Sound Field Reproduction 283\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 283\u003c\/p\u003e \u003cp\u003e6.2 Problem Statement 284\u003c\/p\u003e \u003cp\u003e6.2.1 Concept of Sound Field Reproduction 284\u003c\/p\u003e \u003cp\u003e6.2.2 Objective of Sound Field Reproduction 284\u003c\/p\u003e \u003cp\u003e6.3 Reproduction of One-Dimensional Sound Field 286\u003c\/p\u003e \u003cp\u003e6.3.1 Field-Matching Approach 286\u003c\/p\u003e \u003cp\u003e6.3.2 Mode-Matching Approach 288\u003c\/p\u003e \u003cp\u003e6.3.3 Integral Approach 289\u003c\/p\u003e \u003cp\u003e6.3.4 Single-Layer Potential 295\u003c\/p\u003e \u003cp\u003e6.4 Reproduction of a 3D Sound Field 296\u003c\/p\u003e \u003cp\u003e6.4.1 Problem Statement and Associated Variables 296\u003c\/p\u003e \u003cp\u003e6.5 Field-Matching Approach 298\u003c\/p\u003e \u003cp\u003e6.5.1 Inverse Problem 298\u003c\/p\u003e \u003cp\u003e6.5.2 Regularization of an Inverse Problem 305\u003c\/p\u003e \u003cp\u003e6.5.3 Selection of the Regularization Parameter 309\u003c\/p\u003e \u003cp\u003e6.6 Mode-Matching Approach 311\u003c\/p\u003e \u003cp\u003e6.6.1 Encoding and Decoding of Sound Field 311\u003c\/p\u003e \u003cp\u003e6.6.2 Mode-Matching with Plane Waves 313\u003c\/p\u003e \u003cp\u003e6.6.3 Mode-Matching with Spherical Harmonics 320\u003c\/p\u003e \u003cp\u003e6.7 Surface Integral Equations 337\u003c\/p\u003e \u003cp\u003e6.7.1 Source Inside, Listener Inside (V0 ⊂ V , r ∈ V ) 337\u003c\/p\u003e \u003cp\u003e6.7.2 Source Inside, Listener Outside (V0 ⊂ V , r ∈ ) 340\u003c\/p\u003e \u003cp\u003e6.7.3 Source Outside, Listener Outside (V0 ⊂ , r ∈ ) 341\u003c\/p\u003e \u003cp\u003e6.7.4 Source Outside, Listener Inside (V0 ⊂ , r ∈ V ) 342\u003c\/p\u003e \u003cp\u003e6.7.5 Listener on the Control Surface 342\u003c\/p\u003e \u003cp\u003e6.7.6 Summary of Integral Equations 344\u003c\/p\u003e \u003cp\u003e6.7.7 Nonradiating Sound Field and Nonuniqueness Problem 344\u003c\/p\u003e \u003cp\u003e6.8 Single-layer Formula 346\u003c\/p\u003e \u003cp\u003e6.8.1 Single-layer Formula for Exterior Virtual Source 346\u003c\/p\u003e \u003cp\u003e6.8.2 Integral Formulas for Interior Virtual Source 355\u003c\/p\u003e \u003cp\u003eReferences 369\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A Useful Formulas 371\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Fourier Transform 371\u003c\/p\u003e \u003cp\u003eA.1.1 Fourier Transform Table 371\u003c\/p\u003e \u003cp\u003eA.2 Dirac Delta Function 374\u003c\/p\u003e \u003cp\u003eA.3 Derivative of Matrices 374\u003c\/p\u003e \u003cp\u003eA.3.1 Derivative of Real-Valued Matrix 374\u003c\/p\u003e \u003cp\u003eA.3.2 Derivative of Complex-Valued Function 375\u003c\/p\u003e \u003cp\u003eA.3.3 Derivative of Complex Matrix 376\u003c\/p\u003e \u003cp\u003eA.4 Inverse Problem 376\u003c\/p\u003e \u003cp\u003eA.4.1 Overdetermined Linear Equations and Least Squares (LS) Solution 377\u003c\/p\u003e \u003cp\u003eA.4.2 Underdetermined Linear Equations and Minimum-Norm Problem 378\u003c\/p\u003e \u003cp\u003eA.4.3 Method of Lagrange Multiplier 379\u003c\/p\u003e \u003cp\u003eA.4.4 Regularized Least Squares 380\u003c\/p\u003e \u003cp\u003eA.4.5 Singular Value Decomposition 380\u003c\/p\u003e \u003cp\u003eA.4.6 Total Least Squares (TLS) 382\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B Description of Sound Field 385\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB.1 Three-Dimensional Acoustic Wave Equation 385\u003c\/p\u003e \u003cp\u003eB.1.1 Conservation of Mass 385\u003c\/p\u003e \u003cp\u003eB.1.2 Conservation of Momentum 385\u003c\/p\u003e \u003cp\u003eB.1.3 Equation of State 388\u003c\/p\u003e \u003cp\u003eB.1.4 Velocity Potential Function 390\u003c\/p\u003e \u003cp\u003eB.1.5 Complex Intensity 391\u003c\/p\u003e \u003cp\u003eB.1.6 Singular Sources 392\u003c\/p\u003e \u003cp\u003eB.2 Wavenumber Domain Representation of the Rayleigh Integral 398\u003c\/p\u003e \u003cp\u003eB.2.1 Fourier Transform of Free-Field Green’s Function (Weyl’s Identity) 398\u003c\/p\u003e \u003cp\u003eB.2.2 High Frequency Approximation (Stationary Phase Approximation) 399\u003c\/p\u003e \u003cp\u003eB.3 Separation of Variables in Spherical Coordinates 400\u003c\/p\u003e \u003cp\u003eB.3.1 Angle Functions: Associated Legendre Functions 400\u003c\/p\u003e \u003cp\u003eB.3.2 Angle Functions: Spherical Harmonics 402\u003c\/p\u003e \u003cp\u003eB.3.3 Radial Functions 404\u003c\/p\u003e \u003cp\u003eB.3.4 Radial Functions: Spherical Bessel and Hankel Functions 404\u003c\/p\u003e \u003cp\u003eB.3.5 Description of Sound Fields by Spherical Basis Function 408\u003c\/p\u003e \u003cp\u003eB.3.6 Representation of the Green’s Function 409\u003c\/p\u003e \u003cp\u003eReferences 411\u003c\/p\u003e \u003cp\u003eIndex 413\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default 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