Spectral Analysis

This book deals with these parametric methods, first discussing those based on time series models, Capon’s method and its variants, and then estimators based on the notions of sub-spaces. However, the book also deals with the traditional “analog” methods, now called non-parametric methods, which are still the most widely used in practical spectral analysis.

Preface 9 Specific Notations 13 PART I. Tools and Spectral Analysis 15 Chapter 1. Fundamentals 17 Francis CASTANIÉ 1.1. Classes of signals 17 1.2. Representations of signals 23 1.3. Spectral analysis: position of the problem 33 1.4. Bibliography 35 Chapter 2. Digital Signal Processing 37 Éric LE CARPENTIER 2.1. Introduction 37 2.2. Transform properties 38 2.3. Windows 62 2.4. Examples of application 71 2.5. Bibliography 78 Chapter 3. Estimation in Spectral Analysis 79 Olivier BESSON and André FERRARI 3.1. Introduction to estimation 79 3.2. Estimation of 1st and 2nd order moments 92 3.3. Periodogram analysis 97 3.4. Analysis of estimators based on cxx(m) 3.5. Conclusion 108 3.6. Bibliography 108 Chapter 4. Time-Series Models 111 Francis CASTANIÉ 4.1. Introduction 111 4.2. Linear models 113 4.3. Exponential models 123 4.4. Non-linear models 126 4.5. Bibliography 126 PART II. Non-Parametric Methods 129 Chapter 5. Non-Parametric Methods 131 Éric LE CARPENTIER 5.1. Introduction 131 5.2. Estimation of the power spectral density 136 5.3. Generalization to higher order spectra 146 5.4. Bibliography 148 PART III. Parametric Methods 149 Chapter 6. Spectral Analysis by Stationary Time Series Modeling 151 Corinne MAILHES and Francis CASTANIÉ 6.1. Parametric models 151 6.2. Estimation of model parameters 153 6.3. Properties of spectral estimators produced 167 6.4. Bibliography 172 Chapter 7. Minimum Variance 175 Nadine MARTIN 7.1. Principle of the MV method 179 7.2. Properties of the MV estimator 182 7.3. Link with the Fourier estimators 193 7.4. Link with a maximum likelihood estimator 196 7.5. Lagunas methods: normalized and generalized MV 198 7.6. The CAPNORM estimator 206 7.7. Bibliography 209 Chapter 8. Subspace-based Estimators 213 Sylvie MARCOS 8.1. Model, concept of subspace, definition of high resolution 213 8.2. MUSIC 217 8.3. Determination criteria of the number of complex sine waves 223 8.4. The MinNorm method 224 8.5. "Linear" subspace methods 226 8.6. The ESPRIT method 232 8.7. Illustration of subspace-based methods performance 235 8.8. Adaptive research of subspaces 236 8.9. Bibliography 242 Chapter 9. Introduction to Spectral Analysis of Non-Stationary Random Signals 245 Corinne MAILHES and Francis CASTANIÉ 9.1. Evolutive spectra 246 9.2. Non-parametric spectral estimation 248 9.3. Parametric spectral estimation 249 9.4. Bibliography 255 List of Authors 259 Index 261