Mingsian R. Bai, National Tsing Hua University, TaiwanJeong-Guon Ih, Korea Advanced Institute of Science and Technology (KAIST), South KoreaJacob Benesty, University of Quebec, Canada

• Preface xiAcknowledgments xiiiGlossary: Symbols and Abbreviations xv1 Introduction 11.1 Background and Motivation 11.2 Review of Prior Approaches for Noise Identification Problems 31.3 Organization of the Book 4References 52 Theoretical Preliminaries of Acoustics 92.1 Fundamentals of Acoustics 92.2 Sound Field Representation Using Basis Function Expansion 162.3 Sound Field Representation Using Helmholtz Integral Equation 192.4 Inverse Problems and Ill-Posedness 31References 323 Theoretical Preliminaries of Array Signal Processing 333.1 Linear Algebra Basics 333.2 Digital Signal Processing Basics 423.3 Array Signal Processing Basics 643.4 Optimization Algorithms 773.5 Inverse Filtering from a Model Matching Perspective 853.6 Parameter Estimation Theory 883.6.1 Classical Approaches 893.6.2 Bayesian Approaches 90References 934 Farfield Array Signal Processing Algorithms 954.1 Low-Resolution Algorithms 964.1.1 Fourier Beamformer 964.1.2 Time Reversal Beamformer 994.1.3 SIMO-ESIF Algorithm 1004.1.4 Choice of Farfield Array Parameters 1024.2 High-Resolution Algorithms 1024.2.1 Minimum Variance Beamformers 1034.2.2 Optimal Arrays 1084.2.3 DMA Versus GSC 1304.2.4 Auto-Regressive Array Design 1364.2.5 Multiple Signal Classification (MUSIC) 1404.2.6 Choice of Parameters in MUSIC 1444.3 Comparison of the Farfield Algorithms 145References 1505 Nearfield Array Signal Processing Algorithms 1515.1 Fourier NAH 1515.2 Basis Function Model (BFM)-based NAH 1555.2.1 Spherical Waves 1585.2.2 HELS Method: A Single-Point Multipole Method 1605.3 BEM-based NAH (IBEM): Direct and Indirect Formulations 1635.3.1 Direct IBEM Formulation 1635.3.2 Indirect IBEM Formulation 1685.3.3 Detailed Exposition of the Direct BEM-based NAH 1695.4 Equivalent Source Model (ESM)-based NAH 1775.4.1 Indirect ESM 1785.4.2 ESM Combined with BEM-based NAH 1815.4.3 Direct ESM 1915.4.4 Nearfield Equivalent Source Imaging (NESI) 1955.4.5 Kalman Filter-based Algorithm 1965.4.6 Choice of Nearfield Array Parameters 2045.5 Comparison of the Nearfield Algorithms 205References 2086 Practical Implementation 2116.1 Inverse Filter Design 2116.1.1 Model Matching: Ill-Posedness and Regularization 2116.1.2 Window Design 2136.1.3 Parameter Choice Methods (PCM) 2146.2 Multi-Channel Fast Filtering 2166.2.1 The Time-Domain Processing 2186.2.2 The Frequency-Domain Processing 2186.2.3 Comparison of Filtering Approaches 2206.3 Post-Processing 2216.3.1 Acoustic Variables 2216.3.2 Processing of Moving Sources 2236.4 Choice of Distance of Reconstruction and Lattice Spacing 2266.5 Virtual Microphone Technique: Field Interpolation and Extrapolation 2276.5.1 Sound Field Interpolation by ESM 2276.5.2 More Resolution-Enhancing Reconstruction Strategies 2296.6 Choice of Retreat Distance 2346.6.1 Integral Approximation Error vs. Reconstruction Ill-Posedness 2346.6.2 Determination of RD: Golden Section Search 2356.7 Optimization of Sensor Deployment: Uniform vs. Random Array 2446.7.1 Optimal Nearfield Array: Cost Functions 2446.7.2 Optimizing Nearfield Sensor Deployment 2466.7.3 Optimizing Farfield Sensor Deployment 2506.7.4 Array Sensor Deployment in the Measurement Field Revisited 2636.8 System Integration and Experimental Arrangement 281References 2847 Time-Domain MVDR Array Filter for Speech Enhancement 2877.1 Signal Model and Problem Formulation 2877.1.1 Signal Model for Noise Reduction 2887.1.2 Signal Model for Joint Reverberation and Noise Reduction 2897.1.3 Decomposition of the Noise Signal 2907.2 Linear Array Model 2917.3 Performance Measures 2927.3.1 Input SNR 2927.3.2 Output SNR and Array Gain 2937.3.3 Noise Reduction Factor 2957.3.4 Speech Reduction Factor 2957.3.5 Speech Distortion Index 2967.3.6 MSE Criterion 2967.3.7 Discussion 2977.4 MVDR Filter 2987.5 Link With Other Filters 3017.5.1 Link with Wiener 3017.5.2 Link with the LCMV 3037.6 Further Results 3057.6.1 Noncausal Filters 3057.6.2 Noise Reduction with Filtering Matrices 307References 3138 Frequency-Domain Array Beamformers for Noise Reduction 3158.1 Signal Model and Problem Formulation 3158.2 Linear Array Model 3188.3 Performance Measures 3198.3.1 Input SNR 3198.3.2 Output SNR and Array Gain 3208.3.3 Noise Rejection and Desired Signal Cancellation 3228.3.4 Speech Distortion Index 3238.3.5 Beampattern 3248.3.6 Directivity 3258.3.7 White Noise Gain 3268.3.8 MSE Criterion 3268.4 Optimal Beamformers 3278.4.1 Maximum SNR 3278.4.2 Wiener 3288.4.3 MVDR 3328.4.4 Tradeoff 3348.4.5 LCMV 3408.5 Particular Case: Single Microphone 342References 3439 Application Examples 3459.1 Scooter: Transient Sources 3459.2 Compressor 3519.2.1 Test Setup and Measurements 3559.2.2 Optimal Selection of Measurement Points Using EfI Method 3579.2.3 Reconstructed Source Parameters 3579.2.4 Summary and Conclusions 3629.3 Vacuum Cleaner 3649.3.1 Experimental Setup and Measurements 3649.3.2 Regeneration of Field Data 3649.3.3 Reconstruction of Source Field 3699.3.4 Summary and Conclusions 3709.4 Automotive Internal Combustion Engine 3709.4.1 Experimental Setup and Boundary Element Modeling 3719.4.2 Regeneration of Field Data 3749.4.3 Reconstruction of Source Field 3799.4.4 Post Processing: Power Contribution Analysis of Engine Parts 3809.4.5 Summary and Conclusions 3849.5 Transient Wave Propagation Over an Impacted Thin Plate 3859.5.1 Vibrational Response of an Impacted Thin Plate 3869.5.2 Experimental Setup and Signal Conditioning 3879.5.3 Effect of Numerical Treatments 3909.5.4 Calculation of Structural Intensity Field 3939.6 IT Equipment 3969.7 Wooden Box 3989.8 Non-contact Modal Analysis 3999.9 Speech Enhancement in Reverberant Environments 3999.9.1 Equivalent Source Inverse Filtering 4059.9.2 Adaptive GSC-Enhanced SIMO–ESIF Algorithm 4069.9.3 Array Performance Measures 4119.9.4 Objective and Subjective Performance Evaluations 4119.10 Impact Localization and Haptic Feedback for a Touch Panel 4179.10.1 Bending Waves in a Finite Thin Plate 4189.10.2 Impact Source Localization and Haptic Feedback 4199.10.3 Experimental Investigations 4209.11 Intelligent Stethoscope: Blind Beamforming 4309.12 Rendering and Control of Sound Field by Array Speakers 4339.12.1 Various Methods for Sound Reproduction and Field Rendering 4339.12.2 Basic Theory of Sound Field Rendering by Inverse Design Concept 4419.12.3 Test Examples of Sound Field Rendering by Array Speakers 4459.12.4 Concluding Remarks 4629.13 Sound Field Reconstruction Using ESM and BFM 4639.13.1 Introduction 4639.13.2 ESM-Based Approach 4639.13.3 Virtual Microphone Interpolation Technique 4649.13.4 BFM Interpolation Technique 4659.13.5 Headwind Detection 4669.13.6 Optimization of Retraction Distance 4669.13.7 Numerical Simulations 4679.13.8 Experimental Investigations 4709.13.9 Conclusion 472References 47310 Concluding Remarks and Future Perspectives 47910.1 Concluding Remarks 47910.2 Future Perspectives 48010.2.1 Practical Issues 48010.2.2 Inverse FRF Method 49210.2.3 New Systems 49410.2.4 More Application Scenarios 49710.2.5 Epilog 497References 498Appendix: Acoustic Boundary Element Method 501A.1 Introduction 501A.2 Kirchhoff–Helmholtz Integral Equation 502A.3 Discretization 505A.4 Solution Strategy of Acoustic Boundary Element Method 507A.5 Nonuniqueness Problem 509References 510Index 513

Mingsian R. Bai, National Tsing Hua University, TaiwanJeong-Guon Ih, Korea Advanced Institute of Science and Technology (KAIST), South KoreaJacob Benesty, University of Quebec, Canada

• Preface xiAcknowledgments xiiiGlossary: Symbols and Abbreviations xv1 Introduction 11.1 Background and Motivation 11.2 Review of Prior Approaches for Noise Identification Problems 31.3 Organization of the Book 4References 52 Theoretical Preliminaries of Acoustics 92.1 Fundamentals of Acoustics 92.2 Sound Field Representation Using Basis Function Expansion 162.3 Sound Field Representation Using Helmholtz Integral Equation 192.4 Inverse Problems and Ill-Posedness 31References 323 Theoretical Preliminaries of Array Signal Processing 333.1 Linear Algebra Basics 333.2 Digital Signal Processing Basics 423.3 Array Signal Processing Basics 643.4 Optimization Algorithms 773.5 Inverse Filtering from a Model Matching Perspective 853.6 Parameter Estimation Theory 883.6.1 Classical Approaches 893.6.2 Bayesian Approaches 90References 934 Farfield Array Signal Processing Algorithms 954.1 Low-Resolution Algorithms 964.1.1 Fourier Beamformer 964.1.2 Time Reversal Beamformer 994.1.3 SIMO-ESIF Algorithm 1004.1.4 Choice of Farfield Array Parameters 1024.2 High-Resolution Algorithms 1024.2.1 Minimum Variance Beamformers 1034.2.2 Optimal Arrays 1084.2.3 DMA Versus GSC 1304.2.4 Auto-Regressive Array Design 1364.2.5 Multiple Signal Classification (MUSIC) 1404.2.6 Choice of Parameters in MUSIC 1444.3 Comparison of the Farfield Algorithms 145References 1505 Nearfield Array Signal Processing Algorithms 1515.1 Fourier NAH 1515.2 Basis Function Model (BFM)-based NAH 1555.2.1 Spherical Waves 1585.2.2 HELS Method: A Single-Point Multipole Method 1605.3 BEM-based NAH (IBEM): Direct and Indirect Formulations 1635.3.1 Direct IBEM Formulation 1635.3.2 Indirect IBEM Formulation 1685.3.3 Detailed Exposition of the Direct BEM-based NAH 1695.4 Equivalent Source Model (ESM)-based NAH 1775.4.1 Indirect ESM 1785.4.2 ESM Combined with BEM-based NAH 1815.4.3 Direct ESM 1915.4.4 Nearfield Equivalent Source Imaging (NESI) 1955.4.5 Kalman Filter-based Algorithm 1965.4.6 Choice of Nearfield Array Parameters 2045.5 Comparison of the Nearfield Algorithms 205References 2086 Practical Implementation 2116.1 Inverse Filter Design 2116.1.1 Model Matching: Ill-Posedness and Regularization 2116.1.2 Window Design 2136.1.3 Parameter Choice Methods (PCM) 2146.2 Multi-Channel Fast Filtering 2166.2.1 The Time-Domain Processing 2186.2.2 The Frequency-Domain Processing 2186.2.3 Comparison of Filtering Approaches 2206.3 Post-Processing 2216.3.1 Acoustic Variables 2216.3.2 Processing of Moving Sources 2236.4 Choice of Distance of Reconstruction and Lattice Spacing 2266.5 Virtual Microphone Technique: Field Interpolation and Extrapolation 2276.5.1 Sound Field Interpolation by ESM 2276.5.2 More Resolution-Enhancing Reconstruction Strategies 2296.6 Choice of Retreat Distance 2346.6.1 Integral Approximation Error vs. Reconstruction Ill-Posedness 2346.6.2 Determination of RD: Golden Section Search 2356.7 Optimization of Sensor Deployment: Uniform vs. Random Array 2446.7.1 Optimal Nearfield Array: Cost Functions 2446.7.2 Optimizing Nearfield Sensor Deployment 2466.7.3 Optimizing Farfield Sensor Deployment 2506.7.4 Array Sensor Deployment in the Measurement Field Revisited 2636.8 System Integration and Experimental Arrangement 281References 2847 Time-Domain MVDR Array Filter for Speech Enhancement 2877.1 Signal Model and Problem Formulation 2877.1.1 Signal Model for Noise Reduction 2887.1.2 Signal Model for Joint Reverberation and Noise Reduction 2897.1.3 Decomposition of the Noise Signal 2907.2 Linear Array Model 2917.3 Performance Measures 2927.3.1 Input SNR 2927.3.2 Output SNR and Array Gain 2937.3.3 Noise Reduction Factor 2957.3.4 Speech Reduction Factor 2957.3.5 Speech Distortion Index 2967.3.6 MSE Criterion 2967.3.7 Discussion 2977.4 MVDR Filter 2987.5 Link With Other Filters 3017.5.1 Link with Wiener 3017.5.2 Link with the LCMV 3037.6 Further Results 3057.6.1 Noncausal Filters 3057.6.2 Noise Reduction with Filtering Matrices 307References 3138 Frequency-Domain Array Beamformers for Noise Reduction 3158.1 Signal Model and Problem Formulation 3158.2 Linear Array Model 3188.3 Performance Measures 3198.3.1 Input SNR 3198.3.2 Output SNR and Array Gain 3208.3.3 Noise Rejection and Desired Signal Cancellation 3228.3.4 Speech Distortion Index 3238.3.5 Beampattern 3248.3.6 Directivity 3258.3.7 White Noise Gain 3268.3.8 MSE Criterion 3268.4 Optimal Beamformers 3278.4.1 Maximum SNR 3278.4.2 Wiener 3288.4.3 MVDR 3328.4.4 Tradeoff 3348.4.5 LCMV 3408.5 Particular Case: Single Microphone 342References 3439 Application Examples 3459.1 Scooter: Transient Sources 3459.2 Compressor 3519.2.1 Test Setup and Measurements 3559.2.2 Optimal Selection of Measurement Points Using EfI Method 3579.2.3 Reconstructed Source Parameters 3579.2.4 Summary and Conclusions 3629.3 Vacuum Cleaner 3649.3.1 Experimental Setup and Measurements 3649.3.2 Regeneration of Field Data 3649.3.3 Reconstruction of Source Field 3699.3.4 Summary and Conclusions 3709.4 Automotive Internal Combustion Engine 3709.4.1 Experimental Setup and Boundary Element Modeling 3719.4.2 Regeneration of Field Data 3749.4.3 Reconstruction of Source Field 3799.4.4 Post Processing: Power Contribution Analysis of Engine Parts 3809.4.5 Summary and Conclusions 3849.5 Transient Wave Propagation Over an Impacted Thin Plate 3859.5.1 Vibrational Response of an Impacted Thin Plate 3869.5.2 Experimental Setup and Signal Conditioning 3879.5.3 Effect of Numerical Treatments 3909.5.4 Calculation of Structural Intensity Field 3939.6 IT Equipment 3969.7 Wooden Box 3989.8 Non-contact Modal Analysis 3999.9 Speech Enhancement in Reverberant Environments 3999.9.1 Equivalent Source Inverse Filtering 4059.9.2 Adaptive GSC-Enhanced SIMO–ESIF Algorithm 4069.9.3 Array Performance Measures 4119.9.4 Objective and Subjective Performance Evaluations 4119.10 Impact Localization and Haptic Feedback for a Touch Panel 4179.10.1 Bending Waves in a Finite Thin Plate 4189.10.2 Impact Source Localization and Haptic Feedback 4199.10.3 Experimental Investigations 4209.11 Intelligent Stethoscope: Blind Beamforming 4309.12 Rendering and Control of Sound Field by Array Speakers 4339.12.1 Various Methods for Sound Reproduction and Field Rendering 4339.12.2 Basic Theory of Sound Field Rendering by Inverse Design Concept 4419.12.3 Test Examples of Sound Field Rendering by Array Speakers 4459.12.4 Concluding Remarks 4629.13 Sound Field Reconstruction Using ESM and BFM 4639.13.1 Introduction 4639.13.2 ESM-Based Approach 4639.13.3 Virtual Microphone Interpolation Technique 4649.13.4 BFM Interpolation Technique 4659.13.5 Headwind Detection 4669.13.6 Optimization of Retraction Distance 4669.13.7 Numerical Simulations 4679.13.8 Experimental Investigations 4709.13.9 Conclusion 472References 47310 Concluding Remarks and Future Perspectives 47910.1 Concluding Remarks 47910.2 Future Perspectives 48010.2.1 Practical Issues 48010.2.2 Inverse FRF Method 49210.2.3 New Systems 49410.2.4 More Application Scenarios 49710.2.5 Epilog 497References 498Appendix: Acoustic Boundary Element Method 501A.1 Introduction 501A.2 Kirchhoff–Helmholtz Integral Equation 502A.3 Discretization 505A.4 Solution Strategy of Acoustic Boundary Element Method 507A.5 Nonuniqueness Problem 509References 510Index 513

Mingsian R. Bai, National Tsing Hua University, TaiwanJeong-Guon Ih, Korea Advanced Institute of Science and Technology (KAIST), South KoreaJacob Benesty, University of Quebec, Canada

• Preface xiAcknowledgments xiiiGlossary: Symbols and Abbreviations xv1 Introduction 11.1 Background and Motivation 11.2 Review of Prior Approaches for Noise Identification Problems 31.3 Organization of the Book 4References 52 Theoretical Preliminaries of Acoustics 92.1 Fundamentals of Acoustics 92.2 Sound Field Representation Using Basis Function Expansion 162.3 Sound Field Representation Using Helmholtz Integral Equation 192.4 Inverse Problems and Ill-Posedness 31References 323 Theoretical Preliminaries of Array Signal Processing 333.1 Linear Algebra Basics 333.2 Digital Signal Processing Basics 423.3 Array Signal Processing Basics 643.4 Optimization Algorithms 773.5 Inverse Filtering from a Model Matching Perspective 853.6 Parameter Estimation Theory 883.6.1 Classical Approaches 893.6.2 Bayesian Approaches 90References 934 Farfield Array Signal Processing Algorithms 954.1 Low-Resolution Algorithms 964.1.1 Fourier Beamformer 964.1.2 Time Reversal Beamformer 994.1.3 SIMO-ESIF Algorithm 1004.1.4 Choice of Farfield Array Parameters 1024.2 High-Resolution Algorithms 1024.2.1 Minimum Variance Beamformers 1034.2.2 Optimal Arrays 1084.2.3 DMA Versus GSC 1304.2.4 Auto-Regressive Array Design 1364.2.5 Multiple Signal Classification (MUSIC) 1404.2.6 Choice of Parameters in MUSIC 1444.3 Comparison of the Farfield Algorithms 145References 1505 Nearfield Array Signal Processing Algorithms 1515.1 Fourier NAH 1515.2 Basis Function Model (BFM)-based NAH 1555.2.1 Spherical Waves 1585.2.2 HELS Method: A Single-Point Multipole Method 1605.3 BEM-based NAH (IBEM): Direct and Indirect Formulations 1635.3.1 Direct IBEM Formulation 1635.3.2 Indirect IBEM Formulation 1685.3.3 Detailed Exposition of the Direct BEM-based NAH 1695.4 Equivalent Source Model (ESM)-based NAH 1775.4.1 Indirect ESM 1785.4.2 ESM Combined with BEM-based NAH 1815.4.3 Direct ESM 1915.4.4 Nearfield Equivalent Source Imaging (NESI) 1955.4.5 Kalman Filter-based Algorithm 1965.4.6 Choice of Nearfield Array Parameters 2045.5 Comparison of the Nearfield Algorithms 205References 2086 Practical Implementation 2116.1 Inverse Filter Design 2116.1.1 Model Matching: Ill-Posedness and Regularization 2116.1.2 Window Design 2136.1.3 Parameter Choice Methods (PCM) 2146.2 Multi-Channel Fast Filtering 2166.2.1 The Time-Domain Processing 2186.2.2 The Frequency-Domain Processing 2186.2.3 Comparison of Filtering Approaches 2206.3 Post-Processing 2216.3.1 Acoustic Variables 2216.3.2 Processing of Moving Sources 2236.4 Choice of Distance of Reconstruction and Lattice Spacing 2266.5 Virtual Microphone Technique: Field Interpolation and Extrapolation 2276.5.1 Sound Field Interpolation by ESM 2276.5.2 More Resolution-Enhancing Reconstruction Strategies 2296.6 Choice of Retreat Distance 2346.6.1 Integral Approximation Error vs. Reconstruction Ill-Posedness 2346.6.2 Determination of RD: Golden Section Search 2356.7 Optimization of Sensor Deployment: Uniform vs. Random Array 2446.7.1 Optimal Nearfield Array: Cost Functions 2446.7.2 Optimizing Nearfield Sensor Deployment 2466.7.3 Optimizing Farfield Sensor Deployment 2506.7.4 Array Sensor Deployment in the Measurement Field Revisited 2636.8 System Integration and Experimental Arrangement 281References 2847 Time-Domain MVDR Array Filter for Speech Enhancement 2877.1 Signal Model and Problem Formulation 2877.1.1 Signal Model for Noise Reduction 2887.1.2 Signal Model for Joint Reverberation and Noise Reduction 2897.1.3 Decomposition of the Noise Signal 2907.2 Linear Array Model 2917.3 Performance Measures 2927.3.1 Input SNR 2927.3.2 Output SNR and Array Gain 2937.3.3 Noise Reduction Factor 2957.3.4 Speech Reduction Factor 2957.3.5 Speech Distortion Index 2967.3.6 MSE Criterion 2967.3.7 Discussion 2977.4 MVDR Filter 2987.5 Link With Other Filters 3017.5.1 Link with Wiener 3017.5.2 Link with the LCMV 3037.6 Further Results 3057.6.1 Noncausal Filters 3057.6.2 Noise Reduction with Filtering Matrices 307References 3138 Frequency-Domain Array Beamformers for Noise Reduction 3158.1 Signal Model and Problem Formulation 3158.2 Linear Array Model 3188.3 Performance Measures 3198.3.1 Input SNR 3198.3.2 Output SNR and Array Gain 3208.3.3 Noise Rejection and Desired Signal Cancellation 3228.3.4 Speech Distortion Index 3238.3.5 Beampattern 3248.3.6 Directivity 3258.3.7 White Noise Gain 3268.3.8 MSE Criterion 3268.4 Optimal Beamformers 3278.4.1 Maximum SNR 3278.4.2 Wiener 3288.4.3 MVDR 3328.4.4 Tradeoff 3348.4.5 LCMV 3408.5 Particular Case: Single Microphone 342References 3439 Application Examples 3459.1 Scooter: Transient Sources 3459.2 Compressor 3519.2.1 Test Setup and Measurements 3559.2.2 Optimal Selection of Measurement Points Using EfI Method 3579.2.3 Reconstructed Source Parameters 3579.2.4 Summary and Conclusions 3629.3 Vacuum Cleaner 3649.3.1 Experimental Setup and Measurements 3649.3.2 Regeneration of Field Data 3649.3.3 Reconstruction of Source Field 3699.3.4 Summary and Conclusions 3709.4 Automotive Internal Combustion Engine 3709.4.1 Experimental Setup and Boundary Element Modeling 3719.4.2 Regeneration of Field Data 3749.4.3 Reconstruction of Source Field 3799.4.4 Post Processing: Power Contribution Analysis of Engine Parts 3809.4.5 Summary and Conclusions 3849.5 Transient Wave Propagation Over an Impacted Thin Plate 3859.5.1 Vibrational Response of an Impacted Thin Plate 3869.5.2 Experimental Setup and Signal Conditioning 3879.5.3 Effect of Numerical Treatments 3909.5.4 Calculation of Structural Intensity Field 3939.6 IT Equipment 3969.7 Wooden Box 3989.8 Non-contact Modal Analysis 3999.9 Speech Enhancement in Reverberant Environments 3999.9.1 Equivalent Source Inverse Filtering 4059.9.2 Adaptive GSC-Enhanced SIMO–ESIF Algorithm 4069.9.3 Array Performance Measures 4119.9.4 Objective and Subjective Performance Evaluations 4119.10 Impact Localization and Haptic Feedback for a Touch Panel 4179.10.1 Bending Waves in a Finite Thin Plate 4189.10.2 Impact Source Localization and Haptic Feedback 4199.10.3 Experimental Investigations 4209.11 Intelligent Stethoscope: Blind Beamforming 4309.12 Rendering and Control of Sound Field by Array Speakers 4339.12.1 Various Methods for Sound Reproduction and Field Rendering 4339.12.2 Basic Theory of Sound Field Rendering by Inverse Design Concept 4419.12.3 Test Examples of Sound Field Rendering by Array Speakers 4459.12.4 Concluding Remarks 4629.13 Sound Field Reconstruction Using ESM and BFM 4639.13.1 Introduction 4639.13.2 ESM-Based Approach 4639.13.3 Virtual Microphone Interpolation Technique 4649.13.4 BFM Interpolation Technique 4659.13.5 Headwind Detection 4669.13.6 Optimization of Retraction Distance 4669.13.7 Numerical Simulations 4679.13.8 Experimental Investigations 4709.13.9 Conclusion 472References 47310 Concluding Remarks and Future Perspectives 47910.1 Concluding Remarks 47910.2 Future Perspectives 48010.2.1 Practical Issues 48010.2.2 Inverse FRF Method 49210.2.3 New Systems 49410.2.4 More Application Scenarios 49710.2.5 Epilog 497References 498Appendix: Acoustic Boundary Element Method 501A.1 Introduction 501A.2 Kirchhoff–Helmholtz Integral Equation 502A.3 Discretization 505A.4 Solution Strategy of Acoustic Boundary Element Method 507A.5 Nonuniqueness Problem 509References 510Index 513