[eBook Code] Digital Spectral Analysis (eBook Code, 1st)

Preface xiii

PART 1. TOOLS AND SPECTRAL ANALYSIS 1

Chapter 1. Fundamentals 3
Francis CASTANIÉ

1.1. Classes of signals 3

1.2. Representations of signals 9

1.3. Spectral analysis: position of the problem 20

1.4. Bibliography 21

Chapter 2. Digital Signal Processing 23
Éric LE CARPENTIER

2.1. Introduction 23

2.2. Transform properties 24

2.3. Windows 49

2.4. Examples of application 57

2.5. Bibliography 64

Chapter 3. Introduction to Estimation Theory with Application in Spectral Analysis 67
Olivier BESSON and André FERRARI

3.1. Introduction 67

3.2. Covariance-based estimation 86

3.3. Performance assessment of some spectral estimators 95

3.4. Bibliography 102

Chapter 4. Time-Series Models 105
Francis CASTANIÉ

4.1. Introduction 105

4.2. Linear models 107

4.3. Exponential models 117

4.4. Nonlinear models 120

4.5. Bibliography 121

PART 2. NON-PARAMETRIC METHODS 123

Chapter 5. Non-Parametric Methods 125
Éric LE CARPENTIER

5.1. Introduction 125

5.2. Estimation of the power spectral density 130

5.3. Generalization to higher-order spectra 141

5.4. Bibliography 142

PART 3. PARAMETRIC METHODS 143

Chapter 6. Spectral Analysis by Parametric Modeling145
Corinne MAILHES and Francis CASTANIÉ

6.1. Which kind of parametric models? 145

6.2. AR modeling 146

6.3. ARMA modeling 154

6.4. Prony modeling 156

6.5. Order selection criteria 158

6.6. Examples of spectral analysis using parametric modeling 162

6.7. Bibliography 166

Chapter 7. Minimum Variance 169
Nadine MARTIN

7.1. Principle of the MV method . . 174

7.2. Properties of the MV estimator 177

7.3. Link with the Fourier estimators 188

7.4. Link with a maximum likelihood estimator 190

7.5. Lagunas methods: normalized MV and generalized MV 192

7.6. A new estimator: the CAPNORM estimator 200

7.7. Bibliography 204

Chapter 8. Subspace-Based Estimators and Application to Partially Known Signal Subspaces 207
Sylvie MARCOS and Rémy BOYER

8.1. Model, concept of subspace, definition of high resolution 207

8.2. MUSIC 211

8.3. Determination criteria of the number of complex sine waves 216

8.4. The MinNorm method 217

8.5. “Linear” subspace methods 219

8.6. The ESPRIT method 223

8.7. Illustration of the subspace-based methods performance 226

8.8. Adaptive research of subspaces 229

8.9. Integrating a priori known frequencies into the MUSIC criterion. 233

8.10. Bibliography 243

PART 4. ADVANCED CONCEPTS 251

Chapter 9. Multidimensional Harmonic Retrieval: Exact, Asymptotic, and Modified Cramér-Rao Bounds 253
Rémy BOYER

9.1. Introduction 253

9.2. CanDecomp/Parafac decomposition of the multidimensional
harmonic model 255

9.3. CRB for the multidimensional harmonic model 257

9.4. Modified CRB for the multidimensional harmonic model 266

9.5. Conclusion 272

9.6. Appendices 273

9.7. Bibliography 284

Chapter 10. Introduction to Spectral Analysis of Non-Stationary Random Signals 287
Corinne MAILHES and Francis CASTANIÉ

10.1. Evolutive spectra 288

10.2. Non-parametric spectral estimation 290

10.3. Parametric spectral estimation 291

10.4. Bibliography 297

Chapter 11. Spectral Analysis of Non-uniformly Sampled Signals 301
Arnaud RIVOIRA and Gilles FLEURY

11.1. Applicative context 301

11.2. Theoretical framework 302

11.3. Generation of a randomly sampled stochastic process 302

11.4. Spectral analysis using undated samples 305

11.5. Spectral analysis using dated samples 309

11.6. Perspectives 314

11.7. Bibliography 315

Chapter 12. Space–Time Adaptive Processing 317
Laurent SAVY and François LE CHEVALIER

12.1. STAP, spectral analysis, and radar signal processing 319

12.2. Space–time processing as a spectral estimation problem 327

12.3. STAP architectures 334

12.4. Relative advantages of pre-Doppler and post-Doppler STAP 354

12.5. Conclusion 358

12.6. Bibliography 359

12.7. Glossary 360

Chapter 13. Particle Filtering and Tracking of Varying Sinusoids 361
David BONACCI

13.1. Particle filtering 361

13.2. Application to spectral analysis 370

13.3. Bibliography 375

List of Authors 377

Index 379