Spectral Analysis Parametric and Non-Parametric Digital Methods

by Castanié; , Francis

• ISBN13: 9781905209057
• ISBN10: 1905209053
• Edition: 1st
• Format: Hardcover
• Copyright: 2006-06-05
• Publisher: Wiley-ISTE

Summary

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.

Author Biography

Francis CastaniT is the director of the Research Laboratory Telecommunications for Space and Aeronautics.

Table of Contents

Preface	9	(4)
Specific Notations	13	(2)
PART I. Tools and Spectral Analysis	15	(114)
Chapter 1. Fundamentals	17	(20)
Francis CASTANIÉ
1.1. Classes of signals	17	(6)
1.1.1. Deterministic signals	17	(3)
1.1.2. Random signals	20	(3)
1.2. Representations of signals	23	(10)
1.2.1. Representations of deterministic signals	23	(1)
1.2.1.1. Complete representations	23	(1)
1.2.1.2. Partial representations	25	(2)
1.2.2. Representations of random signals	27	(1)
1.2.2.1. General approach	27	(1)
1.2.2.2. 2nd order representations	28	(1)
1.2.2.3. Higher order representations	32	(1)
1.3. Spectral analysis: position of the problem	33	(2)
1.4. Bibliography	35	(2)
Chapter 2. Digital Signal Processing	37	(42)
Éric LE CARPENTIER
2.1. Introduction	37	(1)
2.2. Transform properties	38	(24)
2.2.1. Some useful functions and series	38	(5)
2.2.2. Fourier transform	43	(4)
2.2.3. Fundamental properties	47	(1)
2.2.4. Convolution sum	48	(2)
2.2.5. Energy conservation (Parseval's theorem)	50	(1)
2.2.6. Other properties	51	(2)
2.2.7. Examples	53	(2)
2.2.8. Sampling	55	(4)
2.2.9. Practical calculation, FFT	59	(3)
2.3. Windows	62	(9)
2.4. Examples of application	71	(7)
2.4.1. LTI systems identification	71	(4)
2.4.2. Monitoring spectral lines	75	(1)
2.4.3. Spectral analysis of the coefficient of tide fluctuation	76	(2)
2.5. Bibliography	78	(1)
Chapter 3. Estimation in Spectral Analysis	79	(32)
Olivier BESSON and André FERRARI
3.1. Introduction to estimation	79	(13)
3.1.1. Formalization of the problem	79	(2)
3.1.2. Cramér-Rao bounds	81	(5)
3.1.3. Sequence of estimators	86	(3)
3.1.4. Maximum likelihood estimation	89	(3)
3.2. Estimation of 1st and 2nd order moments	92	(5)
3.3. Periodogram analysis	97	(4)
3.4. Analysis of estimators based on cxx(m)	101	(7)
3.4.1. Estimation of parameters of an AR model	103	(3)
3.4.2. Estimation of a noisy cisoid by MUSIC	106	(2)
3.5. Conclusion	108	(1)
3.6. Bibliography	108	(3)
Chapter 4. Time-Series Models	111	(18)
Francis CASTANIÉ
4.1. Introduction	111	(2)
4.2. Linear models	113	(10)
4.2.1. Stationary linear models	113	(3)
4.2.2. Properties	116	(1)
4.2.2.1. Stationarity	116	(1)
4.2.2.2. Moments and spectra	117	(1)
4.2.2.3. Relation with Wold's decomposition	119	(1)
4.2.3. Non-stationary linear models	120	(3)
4.3. Exponential models	123	(3)
4.3.1. Deterministic model	123	(1)
4.3.2. Noisy deterministic model	124	(1)
4.3.3. Models of random stationary signals	125	(1)
4.4. Non-linear models	126	(1)
4.5. Bibliography	126	(3)
PART II. Non-Parametric Methods	129	(20)
Chapter 5. Non-Parametric Methods	131	(18)
Éric LE CARPENTIER
5.1. Introduction	131	(5)
5.2. Estimation of the power spectral density	136	(10)
5.2.1. Filter bank method	136	(3)
5.2.2. Periodogram method	139	(3)
5.2.3. Periodogram variants	142	(4)
5.3. Generalization to higher order spectra	146	(2)
5.4. Bibliography	148	(1)
PART III. Parametric Methods	149	(110)
Chapter 6. Spectral Analysis by Stationary Time Series Modeling	151	(24)
Corinne MAILHES and Francis CASTANIÉ
6.1. Parametric models	151	(2)
6.2. Estimation of model parameters	153	(14)
6.2.1. Estimation of AR parameters	153	(7)
6.2.2. Estimation of ARMA parameters	160	(1)
6.2.3. Estimation of Prony parameters	161	(3)
6.2.4. Order selection criteria	164	(3)
6.3. Properties of spectral estimators produced	167	(5)
6.4. Bibliography	172	(3)
Chapter 7. Minimum Variance	175	(38)
Nadine MARTIN
7.1. Principle of the MV method	179	(3)
7.2. Properties of the MV estimator	182	(11)
7.2.1. Expressions of the MV filter	182	(4)
7.2.2. Probability density of the MV estimator	186	(6)
7.2.3. Frequency resolution of the MV estimator	192	(1)
7.3. Link with the Fourier estimators	193	(3)
7.4. Link with a maximum likelihood estimator	196	(2)
7.5. Lagunas methods: normalized and generalized MV	198	(8)
7.5.1. Principle of normalized MV	198	(2)
7.5.2. Spectral refinement of the NMV estimator	200	(2)
7.5.3. Convergence of the NMV estimator	202	(2)
7.5.4. Generalized MV estimator	204	(2)
7.6. The CAPNORM estimator	206	(3)
7.7. Bibliography	209	(4)
Chapter 8. Subspace-based Estimators	213	(32)
Sylvie MARCOS
8.1. Model, concept of subspace, definition of high resolution	213	(4)
8.1.1. Model of signals	213	(1)
8.1.2. Concept of subspaces	214	(2)
8.1.3. Definition of high-resolution	216	(1)
8.1.4. Link with spatial analysis or array processing	217	(1)
8.2. MUSIC	217	(6)
8.2.1. Pseudo-spectral version of MUSIC	220	(1)
8.2.2. Polynomial version of MUSIC	221	(2)
8.3. Determination criteria of the number of complex sine waves	223	(1)
8.4. The MinNorm method	224	(2)
8.5. "Linear" subspace methods	226	(6)
8.5.1. The linear methods	226	(1)
8.5.2. The propagator method	226	(1)
8.5.2.1. Propagator estimation using least squares technique	228	(1)
8.5.2.2. Determination of the propagator in the presence of a white noise	229	(3)
8.6. The ESPRIT method	232	(3)
8.7. Illustration of subspace-based methods performance	235	(1)
8.8. Adaptive research of subspaces	236	(6)
8.9. Bibliography	242	(3)
Chapter 9. Introduction to Spectral Analysis of Non-Stationary Random Signals	245	(14)
Corinne MAILHES and Francis CASTANIÉ
9.1. Evolutive spectra	246	(2)
9.1.1. Definition of the "evolutive spectrum"	246	(1)
9.1.2. Evolutive spectrum properties	247	(1)
9.2. Non-parametric spectral estimation	248	(1)
9.3. Parametric spectral estimation	249	(6)
9.3.1. Local stationary postulate	250	(1)
9.3.2. Elimination of a stationary condition	251	(3)
9.3.3. Application to spectral analysis	254	(1)
9.4. Bibliography	255	(4)
List of Authors	259	(2)
Index	261