Acoustic Array Systems

Preface xi

Acknowledgments xiii

Glossary: Symbols and Abbreviations xv

1 Introduction 1

1.1 Background and Motivation 1

1.2 Review of Prior Approaches for Noise Identification Problems 3

1.3 Organization of the Book 4

References 5

2 Theoretical Preliminaries of Acoustics 9

2.1 Fundamentals of Acoustics 9

2.2 Sound Field Representation Using Basis Function Expansion 16

2.3 Sound Field Representation Using Helmholtz Integral Equation 19

2.4 Inverse Problems and Ill-Posedness 31

References 32

3 Theoretical Preliminaries of Array Signal Processing 33

3.1 Linear Algebra Basics 33

3.2 Digital Signal Processing Basics 42

3.3 Array Signal Processing Basics 64

3.4 Optimization Algorithms 77

3.5 Inverse Filtering from a Model Matching Perspective 85

3.6 Parameter Estimation Theory 88

3.6.1 Classical Approaches 89

3.6.2 Bayesian Approaches 90

References 93

4 Farfield Array Signal Processing Algorithms 95

4.1 Low-Resolution Algorithms 96

4.1.1 Fourier Beamformer 96

4.1.2 Time Reversal Beamformer 99

4.1.3 SIMO-ESIF Algorithm 100

4.1.4 Choice of Farfield Array Parameters 102

4.2 High-Resolution Algorithms 102

4.2.1 Minimum Variance Beamformers 103

4.2.2 Optimal Arrays 108

4.2.3 DMA Versus GSC 130

4.2.4 Auto-Regressive Array Design 136

4.2.5 Multiple Signal Classification (MUSIC) 140

4.2.6 Choice of Parameters in MUSIC 144

4.3 Comparison of the Farfield Algorithms 145

References 150

5 Nearfield Array Signal Processing Algorithms 151

5.1 Fourier NAH 151

5.2 Basis Function Model (BFM)-based NAH 155

5.2.1 Spherical Waves 158

5.2.2 HELS Method: A Single-Point Multipole Method 160

5.3 BEM-based NAH (IBEM): Direct and Indirect Formulations 163

5.3.1 Direct IBEM Formulation 163

5.3.2 Indirect IBEM Formulation 168

5.3.3 Detailed Exposition of the Direct BEM-based NAH 169

5.4 Equivalent Source Model (ESM)-based NAH 177

5.4.1 Indirect ESM 178

5.4.2 ESM Combined with BEM-based NAH 181

5.4.3 Direct ESM 191

5.4.4 Nearfield Equivalent Source Imaging (NESI) 195

5.4.5 Kalman Filter-based Algorithm 196

5.4.6 Choice of Nearfield Array Parameters 204

5.5 Comparison of the Nearfield Algorithms 205

References 208

6 Practical Implementation 211

6.1 Inverse Filter Design 211

6.1.1 Model Matching: Ill-Posedness and Regularization 211

6.1.2 Window Design 213

6.1.3 Parameter Choice Methods (PCM) 214

6.2 Multi-Channel Fast Filtering 216

6.2.1 The Time-Domain Processing 218

6.2.2 The Frequency-Domain Processing 218

6.2.3 Comparison of Filtering Approaches 220

6.3 Post-Processing 221

6.3.1 Acoustic Variables 221

6.3.2 Processing of Moving Sources 223

6.4 Choice of Distance of Reconstruction and Lattice Spacing 226

6.5 Virtual Microphone Technique: Field Interpolation and Extrapolation 227

6.5.1 Sound Field Interpolation by ESM 227

6.5.2 More Resolution-Enhancing Reconstruction Strategies 229

6.6 Choice of Retreat Distance 234

6.6.1 Integral Approximation Error vs. Reconstruction Ill-Posedness 234

6.6.2 Determination of RD: Golden Section Search 235

6.7 Optimization of Sensor Deployment: Uniform vs. Random Array 244

6.7.1 Optimal Nearfield Array: Cost Functions 244

6.7.2 Optimizing Nearfield Sensor Deployment 246

6.7.3 Optimizing Farfield Sensor Deployment 250

6.7.4 Array Sensor Deployment in the Measurement Field Revisited 263

6.8 System Integration and Experimental Arrangement 281

References 284

7 Time-Domain MVDR Array Filter for Speech Enhancement 287

7.1 Signal Model and Problem Formulation 287

7.1.1 Signal Model for Noise Reduction 288

7.1.2 Signal Model for Joint Reverberation and Noise Reduction 289

7.1.3 Decomposition of the Noise Signal 290

7.2 Linear Array Model 291

7.3 Performance Measures 292

7.3.1 Input SNR 292

7.3.2 Output SNR and Array Gain 293

7.3.3 Noise Reduction Factor 295

7.3.4 Speech Reduction Factor 295

7.3.5 Speech Distortion Index 296

7.3.6 MSE Criterion 296

7.3.7 Discussion 297

7.4 MVDR Filter 298

7.5 Link With Other Filters 301

7.5.1 Link with Wiener 301

7.5.2 Link with the LCMV 303

7.6 Further Results 305

7.6.1 Noncausal Filters 305

7.6.2 Noise Reduction with Filtering Matrices 307

References 313

8 Frequency-Domain Array Beamformers for Noise Reduction 315

8.1 Signal Model and Problem Formulation 315

8.2 Linear Array Model 318

8.3 Performance Measures 319

8.3.1 Input SNR 319

8.3.2 Output SNR and Array Gain 320

8.3.3 Noise Rejection and Desired Signal Cancellation 322

8.3.4 Speech Distortion Index 323

8.3.5 Beampattern 324

8.3.6 Directivity 325

8.3.7 White Noise Gain 326

8.3.8 MSE Criterion 326

8.4 Optimal Beamformers 327

8.4.1 Maximum SNR 327

8.4.2 Wiener 328

8.4.3 MVDR 332

8.4.4 Tradeoff 334

8.4.5 LCMV 340

8.5 Particular Case: Single Microphone 342

References 343

9 Application Examples 345

9.1 Scooter: Transient Sources 345

9.2 Compressor 351

9.2.1 Test Setup and Measurements 355

9.2.2 Optimal Selection of Measurement Points Using EfI Method 357

9.2.3 Reconstructed Source Parameters 357

9.2.4 Summary and Conclusions 362

9.3 Vacuum Cleaner 364

9.3.1 Experimental Setup and Measurements 364

9.3.2 Regeneration of Field Data 364

9.3.3 Reconstruction of Source Field 369

9.3.4 Summary and Conclusions 370

9.4 Automotive Internal Combustion Engine 370

9.4.1 Experimental Setup and Boundary Element Modeling 371

9.4.2 Regeneration of Field Data 374

9.4.3 Reconstruction of Source Field 379

9.4.4 Post Processing: Power Contribution Analysis of Engine Parts 380

9.4.5 Summary and Conclusions 384

9.5 Transient Wave Propagation Over an Impacted Thin Plate 385

9.5.1 Vibrational Response of an Impacted Thin Plate 386

9.5.2 Experimental Setup and Signal Conditioning 387

9.5.3 Effect of Numerical Treatments 390

9.5.4 Calculation of Structural Intensity Field 393

9.6 IT Equipment 396

9.7 Wooden Box 398

9.8 Non-contact Modal Analysis 399

9.9 Speech Enhancement in Reverberant Environments 399

9.9.1 Equivalent Source Inverse Filtering 405

9.9.2 Adaptive GSC-Enhanced SIMO-ESIF Algorithm 406

9.9.3 Array Performance Measures 411

9.9.4 Objective and Subjective Performance Evaluations 411

9.10 Impact Localization and Haptic Feedback for a Touch Panel 417

9.10.1 Bending Waves in a Finite Thin Plate 418

9.10.2 Impact Source Localization and Haptic Feedback 419

9.10.3 Experimental Investigations 420

9.11 Intelligent Stethoscope: Blind Beamforming 430

9.12 Rendering and Control of Sound Field by Array Speakers 433

9.12.1 Various Methods for Sound Reproduction and Field Rendering 433

9.12.2 Basic Theory of Sound Field Rendering by Inverse Design Concept 441

9.12.3 Test Examples of Sound Field Rendering by Array Speakers 445

9.12.4 Concluding Remarks 462

9.13 Sound Field Reconstruction Using ESM and BFM 463

9.13.1 Introduction 463

9.13.2 ESM-Based Approach 463

9.13.3 Virtual Microphone Interpolation Technique 464

9.13.4 BFM Interpolation Technique 465

9.13.5 Headwind Detection 466

9.13.6 Optimization of Retraction Distance 466

9.13.7 Numerical Simulations 467

9.13.8 Experimental Investigations 470

9.13.9 Conclusion 472

References 473

10 Concluding Remarks and Future Perspectives 479

10.1 Concluding Remarks 479

10.2 Future Perspectives 480

10.2.1 Practical Issues 480

10.2.2 Inverse FRF Method 492

10.2.3 New Systems 494

10.2.4 More Application Scenarios 497

10.2.5 Epilog 497

References 498

Appendix: Acoustic Boundary Element Method 501

A.1 Introduction 501

A.2 Kirchhoff-Helmholtz Integral Equation 502

A.3 Discretization 505

A.4 Solution Strategy of Acoustic Boundary Element Method 507

A.5 Nonuniqueness Problem 509

References 510

Index 513