Mingsian R. Bai, National Tsing Hua University, Taiwan

Jeong-Guon Ih, Korea Advanced Institute of Science and Technology (KAIST), South Korea

Jacob Benesty, University of Quebec, Canada

Preface

Acknowledgment

1 Introduction

1.1 Background and Motivation

1.2 Review of Prior Arts: Approaches for Noise Identification Problems

1.3 Organization of the Book

References

2 Theoretical Preliminaries of Acoustics

2.1 Fundamentals of Acoustics

2.2 Sound Field Representation Using Basis Function Expansion

2.3 Sound Field Representation Using Helmholtz Integral Equation

2.4 Inverse Problems and Ill-posedness

References

3 Theoretical Preliminaries of Array Signal Processing

3.1 Linear Algebra Basics

3.2 Digital Signal Processing Basics

3.3 Array Signal Processing Basics

3.4 Optimization Algorithms

3.5 Inverse Filtering from a Model Matching Perspective

3.6 Parameter Estimation Theory

References

4 Farfield Array Signal Processing Algorithms

4.1 Low-resolution Algorithms

4.1.1 Fourier Beamformer

4.1.2 Time Reversal Beamformer

4.1.3 SIMO-ESIF Algorithm

4.1.4 Choice of Farfield Array Parameters

4.2 High-resolution Algorithms

4.2.1 Minimum Variance Beamformers

4.2.2 Optimal Arrays

4.2.3 DMA versus GSC

4.2.4 Auto-Regressive Array Design

4.2.5 Multiple Signal Classification (MUSIC)

4.2.6 Choice of Parameters in MUSIC

4.3 Comparison of the Farfield Algorithms

References

5 Nearfield Array Signal Processing Algorithms

5.1 Fourier NAH

5.2 Basis Function Model (BFM)-based NAH

5.2.1. Spherical Waves

5.2.2. HELS Method: A Single-Point Multipole Method

5.3 BEM-based NAH (IBEM): Direct and Indirect Formulations

5.3.1 Direct IBEM Formulation

5.3.2 Indirect IBEM Formulation

5.3.3 Detailed Exposition of the Direct BEM-based NAH

5.3.3.1 Least-Square Solution and Singular Value Decomposition

5.3.3.2 Formulation of BEM-based Acoustical holography

5.3.3.3 Demonstration of SVD of Transfer Matrix for a Radiating Sphere

5.3.3.4 Comparison of the Present Backward Reconstruction with Conventional Forward Reconstruction and the Acoustical holography

5.3.3.5 Ill-posed Nature of Backward Reconstruction

5.3.3.5.1 Mathematical description

5.3.3.5.2 Physical description

5.3.3.6 Wave-vector Filtering

5.3.3.6.1 Range and null space

5.3.3.6.2 Design of wave-vector filter

5.4 Equivalent Source Model (ESM)-based NAH

5.4.1.1 Generalized Equivalent Source Models: A multi-point multipole method

5.4.2 ESM Combined with BEM-based NAH

5.4.2.1 Estimation of Source Strength

5.4.2.2 Radiated Sound Power

5.4.2.3 Numerical Simulations

5.4.2.3.1 Pulsating Sphere

5.4.2.3.2. Baffled Plate on a Parallelepiped Box

5.4.2.4 Epilog

5.4.3 Direct ESM

5.4.4 Nearfield Equivalent Source Imaging (NESI)

5.4.5 Kalman Filter-based Algorithm

5.4.6 Choice of Nearfield Array Parameters

5.5 Comparison of the Nearfield Algorithms

References

6 Practical Implementations

6.1 Inverse Filter Design

6.1.1 Model Matching: Ill-posedness and Regularization

6.1.2 Window Design

6.1.3 Parameter Choice Methods (PCM)

6.2 Multi-channel Fast Filtering

6.2.1 The Time-domain Processing

6.2.2 The Frequency-domain Processing

6.2.3 Comparison of Filtering Approaches

6.3 Post-processing

6.3.1 Acoustic Variables

6.3.2 Processing of Moving Sources

6.4 Choice of Distance of Reconstruction and Lattice Spacing

6.5 Virtual Microphone Technique: Field Interpolation and Extrapolation

6.5.1 Sound Field Interpolation by ESM

6.5.2 More Resolution-Enhancing Reconstruction Strategies

6.6 Choice of Retreat Distance (RD)

6.6.1 Integral Approximation Error vs. Reconstruction Ill-posedness

6.6.2 Determination of RD: Golden Section Search (GSS)

6.7 Optimization of Sensor Deployment: Uniform vs. Random Array

6.7.1 Optimal Nearfield Array: Cost Functions

6.7.2 Optimizing Nearfield Sensor Deployment

6.7.3 Optimizing Farfield Sensor Deployment

6.7.4 Array Sensor Deployment in the Measurement Field Revisited

6.7.4.1 Singularity of the System and Effect of Noise

6.7.4.3 Selection of Sensor Positions Generating Good Transfer Matrix

6.7.4.4 Experimental Investigation

6.8 System Integration and Experimental Arrangement

References 529

7 The Time-domain MVDR Array Filter for Speech Enhancement

7.1 Signal Model and Problem Formulation

7.1.1 Signal Model for Noise Reduction

7.1.2 Signal Model for Joint Reverberation and Noise Reduction

7.1.3 Decomposition of the Noise Signal

7.2 Linear Array Model

7.3 Performance Measures

7.3.1 Input SNR

7.3.2 Output SNR and Array Gain

7.3.3 Noise Reduction Factor

7.3.4 Speech Reduction Factor

7.3.5 Speech Distortion Index

7.3.6 MSE Criterion

7.3.7 Discussion

7.4 MVDR Filter

7.5 Link with Other Filters

7.5.1 Link with Wiener

7.5.2 Link with the LCMV

7.6 Further Results

7.6.1 Noncausal Filters

7.6.2 Noise Reduction with Filtering Matrices

8 Frequency-domain Array Beamformers for Noise Reduction

8.1 Signal Model and Problem Formulation

8.2 Linear Array Model

8.3 Performance Measures

8.3.1 Input SNR

8.3.2 Output SNR and Array Gain

8.3.3 Noise Rejection and Desired Signal Cancellation

8.3.4 Speech Distortion Index

8.3.5 Beampattern

8.3.6 Directivity

8.3.7 White Noise Gain

8.3.8 MSE Criterion

8.4 Optimal Beamformers

8.4.1 Maximum SNR

8.4.2 Wiener

8.4.3 MVDR

8.4.4 Tradeoff

8.4.5 LCMV

8.5 Particular Case: Single Microphone

9 Application Examples

9.1 Scooter: Transient Sources

9.2 Compressor

9.2.1 Test Setup and Measurements

9.2.2 Optimal Selection of Measurement Points Using EfI Method

9.2.3 Reconstructed Source Parameters

9.2.4. Summary and Conclusions

9.3 Vacuum Cleaner

9.3.1 Experimental Setup and Measurements

9.3.2 Regeneration of Field Data

9.3.3 Reconstruction of Source Field

9.3.4 Summary and Conclusions

9.4 Automotive Internal Combustion Engine

9.4.1 Experimental Setup and Boundary Element Modeling

9.4.2 Regeneration of Field Data

9.4.3 Reconstruction of Source Field

9.4.4 Post Processing: Power Contribution Analysis of Engine Parts

9.4.5 Summary and Conclusions

9.5 Transient Wave Propagation over an Impacted Thin Plate

9.5.1 Vibrational response of an impacted thin plate

9.5.2 Experimental setup and signal conditioning

9.5.3 Effect of numerical treatments

9.5.4 Calculation of structural intensity field

9.6 IT Equipment

9.7 Wooden Box

9.8 Non-contact Modal Analysis

9.9 Speech Enhancement in Reverberant Environment

9.9.1 Equivalent Source Inverse Filtering

9.9.2 Adaptive GSC-enhanced SIMO-ESIF Algorithm

9.9.3 Array Performance Measures

9.9.4 Objective and Subjective Performance Evaluations

9.10 Impact Localization and Haptic Feedback for a Touch Panel

9.10.1. Bending Waves in a Finite Thin Plate

9.10.2 Impact Source Localization and Haptic Feedback

9.10.3 Experimental Investigations

9.11 Intelligent Stethoscope: Blind Beamforming

9.12 Rendering and Control of Sound Field by Array Speakers

9.12.1 Various Methods for Sound Reproduction and Field Rendering

9.12.2 Basic Theory of Sound Field Rendering by Inverse Design Concept

9.12.3 Test Examples of Sound Field Rendering by Array Speakers

9.12.4 Concluding Remarks

9.13 Sound Field Reconstruction Using ESM and BFM

9.13.1 Introduction

9.13.2 ESM-Based Approach

9.13.3 Virtual Microphone Interpolation Technique

9.13.4 BFM Interpolation Technique

9.13.5 Headwind Detection

9.13.6 Optimization of Retraction Distance

9.13.7 Numerical Simulations

9.13.8 Experimental Investigations

9.13.9 Conclusion

References

10.1 Concluding Remarks

10.2 Future Perspectives

10.2.1 Practical Issues

10.2.2 Inverse FRF method

10.2.2.1 Introduction

10.2.2.2 Basic Theory

10.2.2.3 Precaution in Measurement Condition

10.2.2.4 Test Examples

10.2.3 New Systems

10.2.4 More Application Scenarios

10.2.5 Epilog

References

Glossary: Symbols and Abbreviations

Appendix A

References

Index