Statistical signal processing: modelling and estimation
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
London [u.a.]
Springer
2002
|
| Series: | Advanced textbooks in control and signal processing
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 331 S. 1 CD-Rom(12 cm) |
| ISBN: | 1852333855 |
Staff View
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Record in the Search Index
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| adam_text |
T. CHONAVEL
TRANSLATED BY JANET ORMROD
STATISTICAL SIGNAL
PROCESSING
MODELLING AND ESTIMATION
SPRINGER
2008
AGI-INFORMATION MANAGEMENT CONSULTANTS
MAY BE USED FOR PERSONAL PURPORSES ONLY OR BY
LIBRARIES ASSOCIATED TO
DANDELON.COM
NETWORK.
CONTENTS
LIST OF NOTATION AND SYMBOLS XV
LIST OF ABBREVIATIONS XIX
1. INTRODUCTION 1
1.1 FOREWORD 1
1.2 MOTIVATION FOR A BOOK IN SIGNAL PROCESSING 1
1.3 A FEW CLASSICAL PROBLEMS IN STATISTICAL SIGNAL PROCESSING. 2
1.4 WHY THIS BOOK? 4
1.5 BOOK CONTENTS 6
1.6 ACKNOWLEDGMENT 8
2. RANDOM PROCESSES 9
2.1 BASIC DEFINITIONS 9
2.1.1 DEFINITION 9
2.1.2 PROBABILITY DISTRIBUTION OF A RANDOM PROCESS 10
2.1.3 KOLMOGOROV'S CONSISTENCY THEOREM 10
2.2 SECOND ORDER PROCESSES 11
2.3 CLASSICAL OPERATIONS IN L
2
(F2,A, DP) 12
2.3.1 MEAN SQUARE CONVERGENCE 13
2.3.2 MEAN SQUARE CONTINUITY 14
2.3.3 MEAN SQUARE DERIVATIVE 14
2.3.4 MEAN SQUARE INTEGRATION 15
2.4 STATIONARITY AND ERGODICITY 17
2.4.1 STATIONARY PROCESSES 17
2.4.2 ERGODIC PROCESSES 17
EXERCISES 20
3. POWER SPECTRUM OF WSS PROCESSES 23
3.1 SPECTRA WITH A DENSITY: POWER SPECTRAL DENSITY (PSD) 23
3.2 SPECTRAL MEASURE 24
EXERCISES 26
VIII CONTENTS
4. SPECTRAL REPRESENTATION OF WSS PROCESSES 31
4.1 STOCHASTIC MEASURES AND STOCHASTIC INTEGRALS 31
4.1.1 DEFINITION 31
4.1.2 MEASURE /I^ ASSOCIATED WITH Z 31
4.1.3 PRINCIPLE OF THE METHOD 32
4.1.4 CONSTRUCTION OF STOCHASTIC INTEGRALS J^(F)(F)DZ(F) . 32
4.2 KOLMOGOROV'S ISOMORPHISM 34
4.3 SPECTRAL REPRESENTATION 34
4.4 SAMPLING 35
EXERCISES 36
5. FILTERING OF WSS PROCESSES 41
5.1 ELEMENTS OF DETERMINISTIC SIGNAL FILTERING 41
5.2 FILTERING OF WSS PROCESSES 42
5.3 COMPARISON OF THE DETERMINISTIC WITH THE STOCHASTIC CASE . 44
5.4 EXAMPLES 45
5.4.1 BANDPASS FILTERS 45
5.4.2 DIFFERENTIATORS 45
5.4.3 LINEAR PARTIAL DIFFERENTIAL EQUATIONS 46
EXERCISES 47
6. IMPORTANT PARTICULAR PROCESSES 51
6.1 GAUSSIAN PROCESSES 51
6.2 POISSON PROCESSES 53
6.3 WHITE NOISE 54
6.3.1 GENERALISED PROCESSES 55
6.3.2 BROWNIAN MOTION 59
6.4 CYCLOSTATIONARY PROCESSES 60
6.5 CIRCULAR PROCESSES 62
6.6 MULTIVARIATE PROCESSES 64
EXERCISES 65
7. NON-LINEAR TRANSFORMS OF PROCESSES 69
7.1 SQUARE LAW DETECTOR AND HARD LIMITER 69
7.1.1 SQUARE LAW DETECTOR 69
7.1.2 HARD LIMITER 70
7.1.3 BUSSGANG'S THEOREM 71
7.2 AMPLITUDE MODULATION 72
7.2.1 PHASE AND QUADRATURE MODULATION 73
7.2.2 ANALYTIC REPRESENTATION AND SSB MODULATION 73
7.2.3 RICE'S REPRESENTATION 74
7.2.4 DEMODULATION IN THE PRESENCE OF NOISE 75
EXERCISES 76
CONTENTS
8. LINEAR PREDICTION OF WSS PROCESSES 79
8.1 DEFINITIONS 79
8.1.1 CONDITIONAL EXPECTATION AND LINEAR PREDICTION 79
8.1.2 INNOVATION PROCESS 80
8.1.3 REGULAR AND SINGULAR PROCESSES 81
8.1.4 EXAMPLES 81
8.2 WOLD'S DECOMPOSITION THEOREM 82
8.3 FINITE PAST LINEAR PREDICTION 84
8.4 CAUSAL FACTORISATION OF A PSD 87
8.4.1 CAUSAL FACTORISATION 87
8.4.2 MINIMUM-PHASE CAUSAL FACTORISATION 88
8.5 THE CONTINUOUS CASE 91
EXERCISES 91
9. PARTICULAR FILTERING TECHNIQUES 95
9.1 WIENER FILTER 95
9.2 KALMAN FILTER 97
9.3 GENERALISATION OF KALMAN FILTER 101
9.4 MATCHED FILTER 105
EXERCISES 107
10. RATIONAL SPECTRAL DENSITIES ILL
10.1 DIFFERENCE EQUATIONS AND RATIONAL SPECTRAL DENSITIES ILL
10.2 SPECTRAL FACTORISATION OF RATIONAL SPECTRA 113
10.3 STATE SPACE REPRESENTATION OF ARMA MODELS 114
EXERCISES 115
11. SPECTRAL IDENTIFICATION OF WSS PROCESSES 119
11.1 SPECTRAL IDENTIFICATION OF ARMA PROCESSES 119
11.1.1 IDENTIFICATION OF THE AR PART 119
11.1.2 IDENTIFICATION OF THE MA PART 120
11.1.3 IDENTIFICATION OF THE STATE SPACE REPRESENTATION 120
11.2 THE TRIGONOMETRIC MOMENT PROBLEM 122
11.2.1 CONDITION OF EXISTENCE OF SOLUTIONS 122
11.2.2 ORTHOGONAL POLYNOMIALS ON THE UNIT CIRCLE 123
11.2.3 PARTICULAR CLASSES OF HOLOMORPHIC FUNCTIONS 126
11.2.4 GENERAL SOLUTION TO THE PROBLEM 127
11.2.5 MAXIMUM ENTROPY SPECTRUM 128
11.3 LINE SPECTRA 129
11.4 LATTICE FILTERS 132
EXERCISES 134
X CONTENTS
12. NON-PARAMETRIC SPECTRAL ESTIMATION 139
12.1 DEFINITIONS 139
12.2 ELEMENTS OF NON-PARAMETRIC ESTIMATION 140
12.2.1 INDEPENDENT DATA SEQUENCES 140
12.2.2 ERGODIC PROCESSES 142
12.3 EMPIRICAL MEAN AND AUTOCOVARIANCES 142
12.3.1 LINEAR PROCESSES 142
12.3.2 EMPIRICAL MEAN 144
12.3.3 EMPIRICAL AUTOCOVARIANCE COEFFICIENTS 145
12.4 EMPIRICAL PSD: THE PERIODOGRAM 147
12.4.1 THE WHITE NOISE CASE 148
12.4.2 THE PERIODOGRAM OF LINEAR PROCESSES 149
12.4.3 THE CASE OF LINE SPECTRA 150
12.5 SMOOTHED PERIODOGRAM 152
12.5.1 INTEGRATED PERIODOGRAM 152
12.5.2 SMOOTHED PERIODOGRAM 153
12.5.3 AVERAGED PERIODOGRAM 156
EXERCISES 156
13. PARAMETRIC SPECTRAL ESTIMATION 159
13.1 INTRODUCTION 159
13.2 ELEMENTS OF PARAMETRIC SPECTRAL ESTIMATION 160
13.2.1 CRAMER-RAO LOWER BOUND (CRLB) 160
13.2.2 MAXIMUM LIKELIHOOD ESTIMATORS 161
13.2.3 MINIMUM VARIANCE LINEAR UNBIASED ESTIMATORS 161
13.2.4 LEAST SQUARES ESTIMATORS 161
13.3 ESTIMATION OF THE AUTOCOVARIANCE COEFFICIENTS 162
13.4 SPECTRUM ESTIMATION OF ARMA MODELS: MEAN SQUARE CRITERIAL63
13.4.1 ESTIMATION OF RATIONAL SPECTRA 163
13.4.2 RATIONAL FILTER SYNTHESIS 166
13.5 ASYMPTOTIC LOG-LIKELIHOOD OF GAUSSIAN PROCESSES 167
13.5.1 GAUSSIAN LOG-LIKELIHOOD 168
13.5.2 ASYMPTOTIC BEHAVIOUR OF THE LOG-LIKELIHOOD 168
13.6 APPROXIMATE MAXIMUM LIKELIHOOD ESTIMATION 172
13.6.1 PRINCIPLE OF THE METHOD 172
13.6.2 CONVERGENCE OF THE ESTIMATORS 174
13.7 MAXIMUM LIKELIHOOD ESTIMATION OF ARMA MODELS 176
13.7.1 THE GENERAL CASE 176
13.7.2 AR MODELS 177
13.7.3 AR MODELS PARAMETERISED BY REFLECTION COEFFICIENTS . . 179
EXERCISES 180
CONTENTS
14. HIGHER ORDER STATISTICS 185
14.1 INTRODUCTION 185
14.2 MOMENTS AND CUMULANTS 186
14.2.1 REAL-VALUED RANDOM VARIABLES 186
14.2.2 REAL AND COMPLEX RANDOM VECTORS 187
14.2.3 PROPERTIES OF MOMENTS AND CUMULANTS 189
14.2.4 EMPIRICAL ESTIMATION OF MOMENTS AND CUMULANTS . 189
14.3 CUMULANTS OF A PROCESS AND CUMULANT SPECTRA 190
14.3.1 CUMULANTS OF A PROCESS 190
14.3.2 CUMULANT SPECTRA 191
14.3.3 HIGHER ORDER WHITE NOISE 192
14.3.4 ESTIMATION OF CUMULANTS AND OF CUMULANT SPECTRA . . . 193
14.3.5 LINEAR FILTERING 193
14.4 ESTIMATION OF A TRANSFER FUNCTION 194
14.4.1 MODEL 194
14.4.2 INTEREST OF HIGHER ORDER STATISTICS 194
14.4.3 DISTANCE CRITERIA 195
14.4.4 DIRECT IDENTIFICATION OF THE FILTER COEFFICIENTS 196
EXERCISES 198
15. BAYESIAN METHODS AND SIMULATION TECHNIQUES 203
15.1 INTRODUCTION 203
15.2 ELEMENTS OF BAYESIAN ESTIMATION 204
15.3 MONTE CARLO METHODS 205
15.3.1 MONTE CARLO INTEGRATION 206
15.3.2 OPTIMISATION 207
15.3.3 SIMULATION OF RANDOM VARIABLES 210
15.4 MCMC (MONTE CARLO MARKOV CHAIN) METHODS 212
15.4.1 MARKOV CHAINS 212
15.4.2 METROPOLIS-HASTINGS ALGORITHM 217
15.4.3 GIBBS SAMPLER 219
15.5 APPLICATION TO FILTERING 221
15.5.1 IMPORTANCE SAMPLING 222
15.5.2 SEQUENTIAL IMPORTANCE SAMPLING 224
15.5.3 DEGENERACY OF THE ALGORITHM 224
15.6 ESTIMATION OF A RATIONAL TRANSFER FUNCTION 225
15.6.1 PRINCIPLE OF THE METHOD 225
15.6.2 ESTIMATION OF THE PARAMETERS 226
EXERCISES 227
16. ADAPTIVE ESTIMATION 231
16.1 CLASSICAL DESCENT TECHNIQUES 231
16.2 PRINCIPLE OF STOCHASTIC OPTIMISATION 233
16.3 LMS AND RLS ALGORITHMS 234
16.4 CONVERGENCE OF LMS AND RLS ALGORITHMS 236
XII CONTENTS
16.4.1 MEAN CONVERGENCE OF THE LMS ALGORITHM 237
16.4.2 ASYMPTOTIC VARIANCE OF THE LMS ALGORITHM 238
16.4.3 CONVERGENCE OF THE RLS ALGORITHM 239
16.5 THE ODE METHOD 240
16.5.1 HYPOTHESES 240
16.5.2 CONVERGENCE OF STOCHASTIC ALGORITHMS 241
16.5.3 ASYMPTOTIC VARIANCE 242
16.5.4 STATIONARY STABLE POINTS OF THE ODE 243
16.5.5 APPLICATION TO THE LMS ALGORITHM 244
EXERCISES 244
A. ELEMENTS OF MEASURE THEORY 249
B. L
2
(F2, A, P) IS A COMPLETE SPACE 253
C. EXTENSION OF A LINEAR OPERATOR 255
D. KOLMOGOROV'S ISOMORPHISM AND SPECTRAL REPRESENTATION. 257
E. WOLD'S DECOMPOSITION 259
F. DIRICHLET'S CRITERION 263
G. VITERBI ALGORITHM 267
H. MINIMUM-PHASE SPECTRAL FACTORISATION OF RATIONAL SPECTRA269
I. COMPATIBILITY OF A GIVEN DATA SET WITH AN AUTOCOVARIANCE
SET 271
1.1 ELEMENTS OF CONVEX ANALYSIS 271
1.2 A NECESSARY AND SUFFICIENT CONDITION 272
J. LEVINSON'S ALGORITHM 277
K. MAXIMUM PRINCIPLE 279
L. ONE STEP EXTENSION OF AN AUTOCOVARIANCE SEQUENCE 281
M. RECURRENCE RELATION UPON P
N
(Z) 283
N. GENERAL SOLUTION TO THE TRIGONOMETRIC MOMENT PROBLEM . 287
O. A CENTRAL LIMIT THEOREM FOR THE EMPIRICAL MEAN 291
P. COVARIANCE OF THE EMPIRICAL AUTOCOVARIANCE COEFFICIENTS . . 293
Q. A CENTRAL LIMIT THEOREM FOR EMPIRICAL AUTOCOVARIANCES . 297
CONTENTS XIII
R. DISTRIBUTION OF THE PERIODOGRAM FOR A WHITE NOISE 299
S. PERIODOGRAM OF A LINEAR PROCESS 301
T. VARIANCE OF THE PERIODOGRAM 303
U. A STRONG LAW OF LARGE NUMBERS (I) 307
V. A STRONG LAW OF LARGE NUMBERS (II) 309
W. PHASE-AMPLITUDE RELATIONSHIP FOR MINIMUM-PHASE CAUSAL
FILTERS 311
X. CONVERGENCE OF THE METROPOLIS-HASTINGS ALGORITHM 313
Y. CONVERGENCE OF THE GIBBS ALGORITHM 315
Z. ASYMPTOTIC VARIANCE OF THE LMS ALGORITHM 319
REFERENCES 321
INDEX 327 |
| any_adam_object | 1 |
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| id | DE-604.BV013738525 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-31T01:02:11Z |
| institution | BVB |
| isbn | 1852333855 |
| language | English French |
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| owner_facet | DE-573 DE-1050 DE-91 DE-BY-TUM DE-634 DE-11 |
| physical | XX, 331 S. 1 CD-Rom(12 cm) |
| publishDate | 2002 |
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| publisher | Springer |
| record_format | marc |
| series2 | Advanced textbooks in control and signal processing |
| spelling | Chonavel, Thierry 1963- Verfasser (DE-588)122099621 aut Statistical signal processing modelling and estimation T. Chonavel London [u.a.] Springer 2002 XX, 331 S. 1 CD-Rom(12 cm) txt rdacontent n rdamedia nc rdacarrier Advanced textbooks in control and signal processing Sinyal işleme - Matematik İstatistik Mathematik Statistik Signal processing Mathematics Statistics Filterung Stochastik (DE-588)4121267-8 gnd rswk-swf Spektralanalyse Stochastik (DE-588)4056125-2 gnd rswk-swf Stochastisches Signal (DE-588)4140374-5 gnd rswk-swf Stochastisches Signal (DE-588)4140374-5 s DE-604 Spektralanalyse Stochastik (DE-588)4056125-2 s Filterung Stochastik (DE-588)4121267-8 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009390892&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chonavel, Thierry 1963- Statistical signal processing modelling and estimation Sinyal işleme - Matematik İstatistik Mathematik Statistik Signal processing Mathematics Statistics Filterung Stochastik (DE-588)4121267-8 gnd Spektralanalyse Stochastik (DE-588)4056125-2 gnd Stochastisches Signal (DE-588)4140374-5 gnd |
| subject_GND | (DE-588)4121267-8 (DE-588)4056125-2 (DE-588)4140374-5 |
| title | Statistical signal processing modelling and estimation |
| title_auth | Statistical signal processing modelling and estimation |
| title_exact_search | Statistical signal processing modelling and estimation |
| title_full | Statistical signal processing modelling and estimation T. Chonavel |
| title_fullStr | Statistical signal processing modelling and estimation T. Chonavel |
| title_full_unstemmed | Statistical signal processing modelling and estimation T. Chonavel |
| title_short | Statistical signal processing |
| title_sort | statistical signal processing modelling and estimation |
| title_sub | modelling and estimation |
| topic | Sinyal işleme - Matematik İstatistik Mathematik Statistik Signal processing Mathematics Statistics Filterung Stochastik (DE-588)4121267-8 gnd Spektralanalyse Stochastik (DE-588)4056125-2 gnd Stochastisches Signal (DE-588)4140374-5 gnd |
| topic_facet | Sinyal işleme - Matematik İstatistik Mathematik Statistik Signal processing Mathematics Statistics Filterung Stochastik Spektralanalyse Stochastik Stochastisches Signal |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009390892&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT chonavelthierry statisticalsignalprocessingmodellingandestimation |