Includes bibliographical references and index.

About the Author xi -- Preface xiii -- Acknowledgments xvii -- Part I ESSENCE OF ACOUSTICS -- 1 Acoustic Wave Equation and Its Basic Physical Measures 3 -- 1.1 Introduction 3 -- 1.2 One-Dimensional Acoustic Wave Equation 3 -- 1.2.1 Impedance 9 -- 1.3 Three-Dimensional Wave Equation 10 -- 1.4 Acoustic Intensity and Energy 11 -- 1.4.1 Complex-Valued Pressure and Intensity 16 -- 1.5 The Units of Sound 18 -- 1.6 Analysis Methods of Linear Acoustic Wave Equation 27 -- 1.6.1 Acoustic Wave Equation and Boundary Condition 28 -- 1.6.2 Eigenfunctions and Modal Expansion Theory 31 -- 1.6.3 Integral Approach Using Green's Function 35 -- 1.7 Solutions of the Wave Equation 39 -- 1.7.1 Plane Wave 40 -- 1.7.2 Spherical Wave 41 -- 1.8 Chapter Summary 46 -- References 46 -- 2 Radiation, Scattering, and Diffraction 49 -- 2.1 Introduction/Study Objectives 49 -- 2.2 Radiation of a Breathing Sphere and a Trembling Sphere 50 -- 2.3 Radiation from a Baffled Piston 58 -- 2.4 Radiation from a Finite Vibrating Plate 65 -- 2.5 Diffraction and Scattering 70 -- 2.6 Chapter Summary 79 -- 2.7 Essentials of Radiation, Scattering, and Diffraction 80 -- 2.7.1 Radiated Sound Field from an Infinitely Baffled Circular Piston 80 -- 2.7.2 Sound Field at an Arbitrary Position Radiated by an Infinitely Baffled Circular Piston 81 -- 2.7.3 Understanding Radiation, Scattering, and Diffraction Using the Kirchhoff / Helmholtz Integral Equation 82 -- 2.7.4 Scattered Sound Field Using the Rayleigh Integral Equation 96 -- References 97 -- Part II SOUND VISUALIZATION -- 3 Acoustic Holography 103 -- 3.1 Introduction 103 -- 3.2 The Methodology of Acoustic Source Identification 103 -- 3.3 Acoustic Holography: Measurement, Prediction, and Analysis 106 -- 3.3.1 Introduction and Problem Definitions 106 -- 3.3.2 Prediction Process 107 -- 3.3.3 Mathematical Derivations of Three Acoustic Holography Methods and Their Discrete Forms 113 -- 3.3.4 Measurement 119 -- 3.3.5 Analysis of Acoustic Holography 124 -- 3.4 Summary 129 -- References 130.

4 Beamforming 137 -- 4.1 Introduction 137 -- 4.2 Problem Statement 138 -- 4.3 Model-Based Beamforming 140 -- 4.3.1 Plane and Spherical Wave Beamforming 140 -- 4.3.2 The Array Configuration 142 -- 4.4 Signal-Based Beamforming 145 -- 4.4.1 Construction of Correlation Matrix in Time Domain 146 -- 4.4.2 Construction of Correlation Matrix in Frequency Domain 151 -- 4.4.3 Correlation Matrix of Multiple Sound Sources 152 -- 4.5 Correlation-Based Scan Vector Design 160 -- 4.5.1 Minimum Variance Beamformer 160 -- 4.5.2 Linear Prediction 164 -- 4.6 Subspace-Based Approaches 170 -- 4.6.1 Basic Principles 170 -- 4.6.2 MUSIC Beamformer 173 -- 4.6.3 ESPRIT 180 -- 4.7 Wideband Processing Technique 182 -- 4.7.1 Frequency-Domain Approach: Mapping to the Beam Space 182 -- 4.7.2 Coherent Subspace Method (CSM) 184 -- 4.7.3 Partial Field Decomposition in Beam Space 185 -- 4.7.4 Time-Domain Technique 190 -- 4.7.5 Moving-Source Localization 198 -- 4.8 Post-Processing Techniques 204 -- 4.8.1 Deconvolution and Beamforming 204 -- 4.8.2 Nonnegativity Constraint 207 -- 4.8.3 Nonnegative Least-Squares Algorithm 209 -- 4.8.4 DAMAS 210 -- References 212 -- Part III SOUND MANIPULATION -- 5 Sound Focusing 219 -- 5.1 Introduction 219 -- 5.2 Descriptions of the Problem of Sound Focusing 221 -- 5.2.1 Free-Field Radiation from Loudspeaker Arrays 221 -- 5.2.2 Descriptions of a Sound Field Depending on the Distance from the Array 221 -- 5.2.3 Fresnel Approximation 223 -- 5.2.4 Farfield Description of the Rayleigh Integral (Fraunhofer Approximation) 225 -- 5.2.5 Descriptors of Directivity 227 -- 5.3 Summing Operator (+) 230 -- 5.3.1 Delay-and-Sum Technique 230 -- 5.3.2 Beam Shaping and Steering 231 -- 5.3.3 Wavenumber Cone and Diffraction Limit 233 -- 5.3.4 Frequency Invariant Radiation Pattern 236 -- 5.3.5 Discrete Array and Grating Lobes 237 -- 5.4 Product Theorem (x) 240 -- 5.4.1 Convolution and Multiplication of Sound Beams 240 -- 5.4.2 On-Axis Pressure Response 243 -- 5.5 Differential Operator and Super-Directivity (-) 245.

5.5.1 Endfire Differential Patterns 245 -- 5.5.2 Combination of Delay-and-Sum and Endfire Differential Patterns 252 -- 5.5.3 Broadside Differential Pattern 252 -- 5.5.4 Combination of the Delay-and-Sum and Broadside Differential Patterns 258 -- 5.6 Optimization with Energy Ratios (÷) 259 -- 5.6.1 Problem Statement 259 -- 5.6.2 Capon's Minimum Variance Estimator (Minimum Variance Beamformer) 261 -- 5.6.3 Acoustic Brightness and Contrast Control 262 -- 5.6.4 Further Analysis of Acoustic Brightness and Contrast Control 273 -- 5.6.5 Application Examples 276 -- References 280 -- 6 Sound Field Reproduction 283 -- 6.1 Introduction 283 -- 6.2 Problem Statement 284 -- 6.2.1 Concept of Sound Field Reproduction 284 -- 6.2.2 Objective of Sound Field Reproduction 284 -- 6.3 Reproduction of One-Dimensional Sound Field 286 -- 6.3.1 Field-Matching Approach 286 -- 6.3.2 Mode-Matching Approach 288 -- 6.3.3 Integral Approach 289 -- 6.3.4 Single-Layer Potential 295 -- 6.4 Reproduction of a 3D Sound Field 296 -- 6.4.1 Problem Statement and Associated Variables 296 -- 6.5 Field-Matching Approach 298 -- 6.5.1 Inverse Problem 298 -- 6.5.2 Regularization of an Inverse Problem 305 -- 6.5.3 Selection of the Regularization Parameter 309 -- 6.6 Mode-Matching Approach 311 -- 6.6.1 Encoding and Decoding of Sound Field 311 -- 6.6.2 Mode-Matching with Plane Waves 313 -- 6.6.3 Mode-Matching with Spherical Harmonics 320 -- 6.7 Surface Integral Equations 337 -- 6.7.1 Source Inside, Listener Inside (V0 ⊂ V , r ∈ V ) 337 -- 6.7.2 Source Inside, Listener Outside (V0 ⊂ V , r ∈ ) 340 -- 6.7.3 Source Outside, Listener Outside (V0 ⊂ , r ∈ ) 341 -- 6.7.4 Source Outside, Listener Inside (V0 ⊂ , r ∈ V ) 342 -- 6.7.5 Listener on the Control Surface 342 -- 6.7.6 Summary of Integral Equations 344 -- 6.7.7 Nonradiating Sound Field and Nonuniqueness Problem 344 -- 6.8 Single-layer Formula 346 -- 6.8.1 Single-layer Formula for Exterior Virtual Source 346 -- 6.8.2 Integral Formulas for Interior Virtual Source 355 -- References 369.

Appendix A Useful Formulas 371 -- A.1 Fourier Transform 371 -- A.1.1 Fourier Transform Table 371 -- A.2 Dirac Delta Function 374 -- A.3 Derivative of Matrices 374 -- A.3.1 Derivative of Real-Valued Matrix 374 -- A.3.2 Derivative of Complex-Valued Function 375 -- A.3.3 Derivative of Complex Matrix 376 -- A.4 Inverse Problem 376 -- A.4.1 Overdetermined Linear Equations and Least Squares (LS) Solution 377 -- A.4.2 Underdetermined Linear Equations and Minimum-Norm Problem 378 -- A.4.3 Method of Lagrange Multiplier 379 -- A.4.4 Regularized Least Squares 380 -- A.4.5 Singular Value Decomposition 380 -- A.4.6 Total Least Squares (TLS) 382 -- Appendix B Description of Sound Field 385 -- B.1 Three-Dimensional Acoustic Wave Equation 385 -- B.1.1 Conservation of Mass 385 -- B.1.2 Conservation of Momentum 385 -- B.1.3 Equation of State 388 -- B.1.4 Velocity Potential Function 390 -- B.1.5 Complex Intensity 391 -- B.1.6 Singular Sources 392 -- B.2 Wavenumber Domain Representation of the Rayleigh Integral 398 -- B.2.1 Fourier Transform of Free-Field Green's Function (Weyl's Identity) 398 -- B.2.2 High Frequency Approximation (Stationary Phase Approximation) 399 -- B.3 Separation of Variables in Spherical Coordinates 400 -- B.3.1 Angle Functions: Associated Legendre Functions 400 -- B.3.2 Angle Functions: Spherical Harmonics 402 -- B.3.3 Radial Functions 404 -- B.3.4 Radial Functions: Spherical Bessel and Hankel Functions 404 -- B.3.5 Description of Sound Fields by Spherical Basis Function 408 -- B.3.6 Representation of the Green's Function 409 -- References 411 -- Index 413.

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