Preface xvii

Acknowledgments xxii

Preface: First Edition xxiii

Acknowledgments: First Edition xxviii

About the Author xxxi

Symbols and Abbreviations xxxiii

1 Introduction to Biomedical Signals 1

1.1 The Nature of Biomedical Signals 1

1.2 Examples of Biomedical Signals 4

1.2.1 The action potential of a cardiac myocyte 4

1.2.2 The action potential of a neuron 11

1.2.3 The electroneurogram (ENG) 12

1.2.4 The electromyogram (EMG) 14

1.2.5 The electrocardiogram (ECG) 21

1.2.6 The electroencephalogram (EEG) 34

1.2.7 Event related potentials (ERPs) 40

1.2.8 The electrogastrogram (EGG) 41

1.2.9 The phonocardiogram (PCG) 42

1.2.10 The carotid pulse 46

1.2.11 Signals from catheter-tip sensors 48

1.2.12 The speech signal 48

1.2.13 The vibromyogram (VMG) 54

1.2.14 The vibroarthrogram (VAG) 54

1.2.15 Otoacoustic emission (OAE) signals 56

1.2.16 Bioacoustic signals 56

1.3 Objectives of Biomedical Signal Analysis 57

1.4 Difficulties in Biomedical Signal Analysis 61

1.5 Why Use CAD? 64

1.6 Remarks 66

1.7 Study Questions and Problems 66

1.8 Laboratory Exercises and Projects 69

2 Concurrent, Coupled, and Correlated Processes 71

2.1 Problem Statement 72

2.2 Illustration of the Problem with Case Studies 72

2.2.1 The ECG and the PCG 72

2.2.2 The PCG and the carotid pulse 73

2.2.3 The ECG and the atrial electrogram 74

2.2.4 Cardiorespiratory interaction 76

2.2.5 The importance of HRV 77

2.2.6 The EMG and VMG 78

2.2.7 The knee joint and muscle vibration signals 79

2.3 Application: Segmentation of the PCG 80

2.4 Application: Diagnosis and Monitoring of Sleep Apnea 81

2.4.1 Monitoring of sleep apnea by polysomnography 83

2.4.2 Home monitoring of sleep apnea 83

2.4.3 Multivariate and multi-organ analysis 84

2.5 Remarks 89

2.6 Study Questions and Problems 89

2.7 Laboratory Exercises and Projects 89

3 Filtering for Removal of Artifacts 91

3.1 Problem Statement 92

3.2 Random, Structured, and Physiological Noise 93

3.2.1 Random noise 93

3.2.2 Structured noise 100

3.2.3 Physiological interference 100

3.2.4 Stationary, nonstationary, and cyclostationary processes 101

3.3 Illustration of the Problem with Case Studies 104

3.3.1 Noise in event-related potentials 104

3.3.2 High frequency noise in the ECG 104

3.3.3 Motion artifact in the ECG 104

3.3.4 Powerline interference in ECG signals 104

3.3.5 Maternal interference in fetal ECG 106

3.3.6 Muscle contraction interference in VAG signals 107

3.3.7 Potential solutions to the problem 109

3.4 Fundamental Concepts of Filtering 110

3.4.1 Linear shift in variant filters 112

3.4.2 Transform domain analysis of signals and systems 124

3.4.3 The pole–zero plot 131

3.4.4 The discrete Fourier transform 133

3.4.5 Properties of the Fourier transform 139

3.5 Time domain Filters 143

3.5.1 Synchronized averaging 143

3.5.2 MA filters 147

3.5.3 Derivative based operators to remove low frequency artifacts 155

3.5.4 Various specifications of a filter 161

3.6 Frequency domain Filters 162

3.6.1 Removal of high frequency noise: Butterworth low pass filters 164

3.6.2 Removal of low frequency noise: Butterworth highpass filters 171

3.6.3 Removal of periodic artifacts: Notch and comb filters 173

3.7 Order-statistic filters 177

3.8 Optimal Filtering: The Wiener Filter 181

3.9 Adaptive Filters for Removal of Interference 196

3.9.1 The adaptive noise canceler 198

3.9.2 The least mean squares adaptive filter 201

3.9.3 The RLS adaptive filter 202

3.10 Selecting an Appropriate Filter 207

3.11 Application: Removal of Artifacts in ERP Signals 211

3.12 Application: Removal of Artifacts in the ECG 215

3.13 Application: Maternal–Fetal ECG 217

3.14 Application: Muscle contraction Interference 218

3.15 Remarks 220

3.16 Study Questions and Problems 222

3.17 Laboratory Exercises and Projects 230

4 Detection of Events 233

4.1 Problem Statement 233

4.2 Illustration of the Problem with Case Studies 234

4.2.1 The P, QRS, and T waves in the ECG 234

4.2.2 The first and second heart sounds 235

4.2.3 The dicrotic notch in the carotid pulse 236

4.2.4 EEG rhythms, waves, and transients 236

4.3 Detection of Events and Waves 239

4.3.1 Derivative based methods for QRS detection 239

4.3.2 The Pan–Tompkins algorithm for QRS detection 243

4.3.3 Detection of the dicrotic notch 247

4.4 Correlation Analysis of EEG Rhythms 249

4.4.1 Detection of EEG rhythms 249

4.4.2 Template matching for EEG spike and wave detection 252

4.4.3 Detection of EEG rhythms related to seizure 254

4.5 Cross-spectral Techniques 255

4.5.1 Coherence analysis of EEG channels 255

4.6 The Matched Filter 260

4.6.1 Derivation of the transfer function of the matched filter 260

4.6.2 Detection of EEG spike and wave complexes 263

4.7 Detection of the P Wave in the ECG 267

4.8 Homomorphic Filtering 269

4.8.1 Generalized linear filtering 270

4.8.2 Homomorphic deconvolution 271

4.8.3 Extraction of the vocal tract response 272

4.9 Application: ECG Rhythm Analysis 281

4.10 Application: Identification of Heart Sounds 284

4.11 Application: Detection of the Aortic Component of S2 286

4.12 Remarks 290

4.13 Study Questions and Problems 291

4.14 Laboratory Exercises and Projects 293

5 Analysis of Waveshape and Waveform Complexity 295

5.1 Problem Statement 296

5.2 Illustration of the Problem with Case Studies 296

5.2.1 The QRS complex in the case of bundle-branch block 296

5.2.2 The effect of myocardial ischemia and infarction on QRS waveshape 296

5.2.3 Ectopic beats 297

5.2.4 Complexity of the EMG interference pattern 297

5.2.5 PCG intensity patterns 297

5.3 Analysis of ERPs 298

5.4 Morphological Analysis of ECG Waves 298

5.4.1 Correlation coefficient 299

5.4.2 The minimum-phase correspondent and signal length 299

5.4.3 ECG waveform analysis 306

5.5 Envelope Extraction and Analysis 307

5.5.1 Amplitude demodulation 309

5.5.2 Synchronized averaging of PCG envelopes 311

5.5.3 The envelogram 311

5.6 Analysis of Activity 314

5.6.1 The RMS value 315

5.6.2 Zero-crossing rate 317

5.6.3 Turns count 317

5.6.4 Form factor 319

5.7 Application: Normal and Ectopic ECG Beats 320

5.8 Application: Analysis of Exercise ECG 321

5.9 Application: Analysis of the EMG in Relation to Force 323

5.10 Application: Analysis of Respiration 327

5.11 Application: Correlates of Muscular Contraction 327

5.12 Application: Statistical Analysis of VAG Signals 329

5.12.1 Acquisition of knee-joint VAG signals 330

5.12.2 Estimation of the PDFs of VAG signals 333

5.12.3 Screening of VAG signals using statistical parameters 336

5.13 Application: Fractal Analysis of the EMG in Relation to Force 337

5.13.1 Fractals in nature 338

5.13.2 Fractal dimension 338

5.13.3 Fractal analysis of physiological signals 340

5.13.4 Fractal analysis of EMG signals 341

5.14 Remarks 343

5.15 Study Questions and Problems 343

5.16 Laboratory Exercises and Projects 346

6 Frequency domain Characterization 349

6.1 Problem Statement 351

6.2 Illustration of the Problem with Case Studies 351

6.2.1 The effect of myocardial elasticity on heart sound spectra 351

6.2.2 Frequency analysis of murmurs to diagnose valvular defects 352

6.3 Estimation of the PSD 356

6.3.1 The periodogram 357

6.3.2 The need for averaging 359

6.3.3 The use of windows: Spectral resolution and leakage 360

6.3.4 Estimation of the ACF 367

6.3.5 Synchronized averaging of PCG spectra 369

6.4 Measures Derived from PSDs 370

6.4.1 Moments of PSD functions 372

6.4.2 Spectral power ratios 375

6.5 Application: Evaluation of Prosthetic Valves 376

6.6 Application: Fractal Analysis of VAG Signals 378

6.6.1 Fractals and the 1/f model 378

6.6.2 FD via power spectral analysis 380

6.6.3 Examples of synthesized fractal signals 381

6.6.4 Fractal analysis of segments of VAG signals 382

6.7 Application: Spectral Analysis of EEG Signals 385

6.8 Remarks 390

6.9 Study Questions and Problems 391

6.10 Laboratory Exercises and Projects 393

7 Modeling Biomedical Systems 397

7.1 Problem Statement 398

7.2 Illustration of the Problem 398

7.2.1 Motor unit firing patterns 398

7.2.2 Cardiac rhythm 399

7.2.3 Formants and pitch in speech 399

7.2.4 Patellofemoral crepitus 401

7.3 Point Processes 401

7.4 Parametric System Modeling 408

7.5 Autoregressive or All-pole Modeling 413

7.5.1 Spectral matching and parameterization 419

7.5.2 Optimal model order 422

7.5.3 AR and cepstral coefficients 425

7.6 Pole-zero Modeling 428

7.6.1 Sequential estimation of poles and zeros 434

7.6.2 Iterative system identification 436

7.6.3 Homomorphic prediction and modeling 441

7.7 Electromechanical Models of Signal Generation 445

7.7.1 Modeling of respiratory sounds 447

7.7.2 Sound generation in coronary arteries 450

7.7.3 Sound generation in knee joints 453

7.8 Application: Heartrate Variability 455

7.9 Application: Spectral Modeling and Analysis of PCG Signals 458

7.10 Application: Coronary Artery Disease 462

7.11 Remarks 463

7.12 Study Questions and Problems 466

7.13 Laboratory Exercises and Projects 467

8 Analysis of Nonstationary and Multicomponent Signals 469

8.1 Problem Statement 470

8.2 Illustration of the Problem with Case Studies 471

8.2.1 Heart sounds and murmurs 471

8.2.2 EEG rhythms and waves 471

8.2.3 Articular cartilage damage and knee-joint vibrations 471

8.3 Time variant Systems 474

8.3.1 Characterization of nonstationary signals and dynamic systems 475

8.4 Fixed Segmentation 478

8.4.1 The short-time Fourier transform 478

8.4.2 Considerations in short-time analysis 482

8.5 Adaptive Segmentation 483

8.5.1 Spectral error measure 486

8.5.2 ACF distance 490

8.5.3 The generalized likelihood ratio 493

8.5.4 Comparative analysis of the ACF, SEM, and GLR methods 494

8.6 Use of Adaptive Filters for Segmentation 497

8.6.1 Monitoring the RLS filter 498

8.6.2 The RLS lattice filter 499

8.7 Wavelets and Time frequency Analysis 508

8.7.1 Approximation of a signal using wavelets 511

8.7.2 Signal decomposition using the Matching Pursuit algorithm 515

8.7.3 Empirical mode decomposition 516

8.7.4 TFDs and their characteristics 519

8.7.5 Decomposition based adaptive TFD 521

8.7.6 Illustrations of application 524

8.8 Separation of Mixtures of Signals 530

8.8.1 Principal component analysis 532

8.8.2 Independent component analysis 544

8.9 Application: Adaptive Segmentation of EEG Signals 547

8.10 Application: Adaptive Segmentation of PCG Signals 553

8.11 Application: Time-varying Analysis of HRV 553

8.12 Application: Detection of Epileptic Seizures in EEG Signals 558

8.13 Application: Analysis of Crying Sounds of Infants 559

8.14 Application: Adaptive Time frequency Analysis of VAG Signals 559

8.15 Remarks 563

8.16 Study Questions and Problems 569

8.17 Laboratory Exercises and Projects 569

9 Pattern Classification and Diagnostic Decision 571

9.1 Problem Statement 572

9.2 Illustration of the Problem with Case Studies 572

9.2.1 Diagnosis of bundle-branch block 572

9.2.2 Normal or ectopic ECG beat? 573

9.2.3 Is there an alpha rhythm? 574

9.2.4 Is a murmur present? 574

9.3 Pattern Classification 575

9.4 Supervised Pattern Classification 575

9.4.1 Discriminant and decision functions 576

9.4.2 Fisher linear discriminant analysis 578

9.4.3 Distance functions 581

9.4.4 The nearest neighbor rule 582

9.5 Unsupervised Pattern Classification 583

9.5.1 Cluster seeking methods 583

9.6 Probabilistic Models and Statistical Decision 587

9.6.1 Likelihood functions and statistical decision 588

9.6.2 Bayes classifier for normal patterns 591

9.7 Logistic Regression Analysis 592

9.8 Neural Networks 593

9.8.1 ANNs with radial basis functions 595

9.9 Measures of Diagnostic Accuracy and Cost 598

9.9.1 Receiver operating characteristics 602

9.9.2 McNemar’s test of symmetry 604

9.10 Reliability of Features, Classifiers, and Decisions 606

9.10.1 Separability of features 607

9.10.2 Feature selection 610

9.10.3 The training and test steps 612

9.11 Application: Normal versus Ectopic ECG Beats 614

9.11.1 Classification with a linear discriminant function 614

9.11.2 Application of the Bayes classifier 619

9.11.3 Classification using the Kmeans method 619

9.12 Application: Detection of Knee joint Cartilage Pathology 620

9.13 Remarks 627

9.14 Study Questions and Problems 630

9.15 Laboratory Exercises and Projects 632

References 633

Index 663

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