Description
Book SynopsisDigital Spectral Analysis provides a single source that offers complete coverage of the spectral analysis domain. This self-contained work includes details on advanced topics that are usually presented in scattered sources throughout the literature.
The theoretical principles necessary for the understanding of spectral analysis are discussed in the first four chapters: fundamentals, digital signal processing, estimation in spectral analysis, and time-series models.
An entire chapter is devoted to the non-parametric methods most widely used in industry.
High resolution methods are detailed in a further four chapters: spectral analysis by stationary time series modeling, minimum variance, and subspace-based estimators.
Finally, advanced concepts are the core of the last four chapters: spectral analysis of non-stationary random signals, space time adaptive processing: irregularly sampled data processing, particle filtering and tracking of varying sinusoids.
Suitable for students, engineers working in industry, and academics at any level, this book provides a rare complete overview of the spectral analysis domain.
Table of ContentsPreface 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
