Higher-order spectra analysis: a nonlinear signal processing framework
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Englewood Cliffs, NJ
Prentice-Hall
1993
|
| Schriftenreihe: | Prentice Hall signal processing series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 537 S. Ill., graph. Darst. |
| ISBN: | 0136782108 |
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| 245 | 1 | 0 | |a Higher-order spectra analysis |b a nonlinear signal processing framework |c Chrysostomos L. Nikias ; Athina P. Petropulu |
| 246 | 1 | 3 | |a Higher order spectra analysis |
| 264 | 1 | |a Englewood Cliffs, NJ |b Prentice-Hall |c 1993 | |
| 300 | |a XXII, 537 S. |b Ill., graph. Darst. | ||
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| 650 | 7 | |a Traitement du signal - Techniques numériques |2 ram | |
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| 650 | 4 | |a Spectrum analysis | |
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Datensatz im Suchindex
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c2?, h
HIGHER - ORDER
SPECTRA ANALYSIS
R^f^NL^EARSlGNAL PROCESSING FRAMEWORK g
Nachrichtentechnische Bibliothek
THD Inv -Nr :
J amp; S%bXd§
Chrysostomos L lNikias
University of Southern California
Athina P Petropulu
Drexel University
PTR Prentice Hall, Englewood Cliffs, New Jersey 07632
CONTENTS
PREFACE xvii
LIST OF SYMBOLS xxi
CHAPTER 1 INTRODUCTION 1
1 1 POWER SPECTRUM 1
1 2 WHY POLYSPECTRA IN SIGNAL PROCESSING? 2
1 3 APPLICATIONS 4
REFERENCES 4
CHAPTER 2 CUMULANT SPECTRA OF STOCHASTIC SIGNALS 7
2 1 INTRODUCTION 7
2 2 MOMENTS AND CUMULANTS 7
221 Definitions 7
222 Relationship Between Moments and Cumulants 9
223 Properties of Moments and Cumulants 12
224 Moments and Cumulants of Stationary Processes 15
225 Variance, Skewness, and Kurtosis Measures 16
226 Time-Reversible Process 17
227 Cross-Cumulants 17
228 Ergodicity and Moments 19
2 3 CUMULANT SPECTRA 20
231 Definition 20
232 Alternative Definition 21
233 Special Cases of Cumulant Spectra t*i i ; 21
234 Variance, Skewness, and Kurtosis Measures 23
235 Time-Reversible Processes 24
236 Non-Gaussian White Noise Processes 24
237 One-Dimensional Slices of Cumulants and their Cumulant
Spectra 26
238 Why Cumulant Spectra and not Moment Spectra 30
239 The nth-Order Coherency Function 31
VI
Contents
2 3 10 Cross-Cumulant Spectra 31
2 3 11 Linear Phase Shifts 33
2 3 12 Complex Regression Coefficients 34
2 3 13 Complex Processes 34
2 3 14 The Wigner Bispectrum 36
2 4 CUMULANT SPECTRA OF NON-GAUSSIAN LINEAR
PROCESSES 37
241 Cumulant Spectra of LTI Systems 37
242 Cumulant Spectra of LTI Systems Driven by White Noise - 38
243 Nonminimum Phase LTI Systems 45
244 Linear Processes with Gaussian and
Non-Gaussian Components 53
245 Poisson Triggered Processes 56
246 Regression Coefficients of Linear Processes 57
2 5 DETECTING AND IDENTIFYING NONLINEAR PROCESSES 58
251 Sinusoidal Processes Applied to Nonlinear Systems 58
252 Quadratic Phase Coupling 59
253 Gaussian Processes Applied to Nonlinear Systems 61
254 Linear Non-Gaussian versus Nonlinear Processes 64
2 6 SUMMARY 64
REFERENCES 66
CHAPTER 3 MOMENT SPECTRA OF DETERMINISTIC SIGNALS 71
3 1 INTRODUCTION 71
311 Energy versus Power Deterministic Signals 71
312 Fourier Analysis of Energy Signals 72
313 Fourier Analysis of Periodic Power Signals 73
314 Finite-Duration versus Periodic Signals 75
3 2 MOMENTS OF ENERGY SIGNALS 78
321 Definition 78
322 Properties 78
Contents
vii
323 Special Cases 80
324 Cross-Moments 83
3 3 MOMENT SPECTRA OF APERIODIC ENERGY SIGNALS 84
331 Definition 85
332 An Alternative Definition 85
333 Special Cases of Moment Spectra 88
334 Scalar Measures of Energy Signals 89
335 Moment Spectra and LTI System Relations 90
336 Phase Conditions 94
337 Cross-Moment Spectra 98
338 The nth-Order Coherency of Energy Signals 99
3 4 MOMENTS OF POWER SIGNALS 100
341 Definition 100
342 Special Cases for Periodic Signals 101
343 Cross-Moments of Periodic Signals 106
3 5 MOMENT SPECTRA OF PERIODIC POWER SIGNALS 107
351 Definition 108
352 An Alternative Definition 109
353 Special Cases of Moment Spectra 110
354 LTI System Relations 116
355 Cross-Moment Spectra 117
356 Higher-Order Coherency Function of Periodic Power Signals 119
357 Finite-Duration versus Periodic Signals:
Moment Spectra Relationships 120
3 6 SUMMARY 121
REFERENCES 121
CHAPTER 4 CONVENTIONAL METHODS FOR THE
ESTIMATION OF HIGHER-ORDER SPECTRA 123
4 1 INTRODUCTION 123
4 2 INDIRECT CLASS OF CONVENTIONAL METHODS 124
Contents
viii
421 Estimation of Higher-Order Statistics 124
422 Estimation of Higher-Order Spectra 125
423 Window Functions 126
4 3 DIRECT CLASS OF CONVENTIONAL METHODS 132
431 The Higher-Order Periodogram 132
432 Direct Estimation of Moment Spectra 136
433 The Zurbenko Method for the Estimation
of Cumulant Spectra 138
4 4 COMPLEX DEMODULATES CLASS OF CONVENTIONAL
METHODS 141
4 5 STATISTICAL PROPERTIES OF CONVENTIONAL METHODS 142
451 Properties of Bispectral Estimates 142
452 Properties of Higher-Order Spectrum Estimation 145
4 6 TEST FOR ALIASING WITH THE BISPECTRUM 147
4 7 BISPECTRUM COMPUTATION ON POLAR RASTERS 149
471 Introduction 149
472 Problem Formulation 150
473 The Direct Approach (DA) 151
474 The Zero-Padding Approach (ZPA) 151
475 The “Super-FFT Approach” (SFA) 153
476 Trispectrum Computation on a Polar Raster 155
477 Extension to Stochastic Signals 158
4 8 SUMMARY 159
REFERENCES 159
CHAPTER 5 HIGHER-ORDER CEPSTRA (POLYCEPSTRA) 163
5 1 INTRODUCTION 163
5 2 THE COMPLEX CEPSTRUM OF DETERMINISTIC ENERGY
SIGNALS 164
521 Signal Assumptions 164
522 Definition 165
523 Properties 166
Contents ix
524 Computation and Phase Unwrapping 167
5 3 THE DIFFERENTIAL CEPSTRUM OF DETERMINISTIC
ENERGY SIGNALS 169
531 Definition 169
532 Properties 170
533 Computation 171
5 4 THE POWER CEPSTRUM OF DETERMINISTIC AND
STOCHASTIC SIGNALS 172
541 Definition 172
542 Properties 173
543 Computation 174
5 5 THE BICEPSTRUM AND TRICEPSTRUM OF DETERMINISTIC
AND STOCHASTIC SIGNALS 177
551 Definition 179
552 Properties 181
553 Computation 182
554 The TVicepstrum 185
5 6 THE CEPSTRUM OF BICOHERENCY 187
561 Definition 189
562 Properties 189
563 Computation 190
564 Computation of A^m\ B^m' from
Second- and Third-Order Statistics 191
5 7 HIGHER-ORDER SPECTRUM FACTORIZATION AND INDEX
FOR LINEARITY 191
5 8 INVERSE FILTER RECONSTRUCTION 193
5 9 THE CROSS-BICEPSTRUM OF DETERMINISTIC
AND STOCHASTIC SIGNALS 200
591 Preliminaries 200
592 Signal Assumptions 203
593 Definition 203
594 Properties 204
X
Contents
595 Computation 205
5 10 ANALYTIC PERFORMANCE EVALUATION OF THE COMPLEX
CEPSTRUM AND BICEPSTRUM 209
5 10 1 Preliminaries and Problem Definition 209
5 10 2 The Complex Cepstrum Evaluation 211
5 10 3 The Bicepstrum Evaluation 214
5 11 SUMMARY 215
REFERENCES 216
CHAPTER 6 NONPARAMETRIC METHODS FOR SIGNAL
RECOVERY FROM HIGHER-ORDER SPECTRA 219
6 1 INTRODUCTION 219
6 2 MAGNITUDE AND PHASE ESTIMATION FROM
HIGHER-ORDER SPECTRA 220
6 3 PHASE RECOVERY ALGORITHMS 220
631 The Brillinger Algorithm 221
632 The Lii-Rosenblatt Algorithm 222
633 The Bartelt-Lohman-Wirnitzer Algorithm 223
634 The Matsuoka-Ulrych Algorithm 224
635 Phase Reconstruction from a 45° Slice of the
Bispectral Phase 228
6 4 PHASE AND MAGNITUDE ALGORITHMS BASED ON
POLYSPECTRA/POLYCEPSTRA PROPERTIES 230
641 Preliminaries 230
642 Bispectrum Signal Reconstruction (BSR) 231
643 Two-Dimensional Phase Unwrapping 233
644 Duality Between Phase and Magnitude Recovery 234
645 Treating Singularities in the Vicinity of the Unit Circle 235
6 5 SIGNAL RECONSTRUCTION FROM ONLY THE PHASE OF
THE BISPECTRUM 237
651 The Importance of Signal Recovery from Partial Information 237
652 Conditions for Signal Reconstruction from the
Phase of the Bicepstrum 239
Contents xi
653 The Bispectrum Iterative Reconstruction Algorithm (BIRA) 240
6 6 SIGNAL RECONSTRUCTION FROM THE BISPECTRUM BASED
ON THE METHOD OF POCS 249
6 7 BLIND DECONVOLUTION USING BIRA 253
671 The Blind Deconvolution Scheme 254
672 Computation of the Differences of Cepstral Coefficients 256
6 8 SUMMARY 259
REFERENCES 261
CHAPTER 7 PARAMETRIC METHODS FOR THE
ESTIMATION OF HIGHER-ORDER SPECTRA 265
7 1 INTRODUCTION 265
7 2 MA METHODS 266
721 Closed Form Solutions 267
722 Optimization Methods 270
723 Parameter Estimation Based on ARMA and AR
Approximations 271
724 The GM Method 276
7 3 NONCAUSAL AR METHODS 278
731 The Huzii Method 278
732 Cumulant Based Solutions 279
7 4 ARMA METHODS 282
741 Estimation of the ARMA Parameters from the System
Impulse Response 282
742 Residual Time Series 284
743 The Double c(q,k) Algorithm 286
744 The Q-Slice Algorithm 291
745 Identification of ARMA Systems Via Second- and Fourth-Order
Cumulant Matching 293
7 5 MODEL ORDER DETERMINATION 295
751 MA Models 295
752 AR Models 304
Contents
xii
753 ARMA Models 307
7 6 SUMMARY 307
REFERENCES 308
CHAPTER 8 DIRECTION OF ARRIVAL ESTIMATION AND ANALYSIS
OF TRANSIENT SIGNALS 313
8 1 INTRODUCTION 313
8 2 TIME DELAY ESTIMATION 314
821 Problem Definition 314
822 Bearing and Range Estimation 315
823 Generalized Cross-Correlation (GCC) Method 317
824 Conventional TDE Methods Based on Third-Order Statistics 322
825 Parametric TDE Method in the Bispectrum Domain 327
826 TDE Method Based on the Cepstrum of the
Cross-Bispectrum 331
827 TDE with the Mean Fourth-Cumulant (MFC) Criterion 332
8 3 BEARING ESTIMATION WITH HIGHER-ORDER STATISTICS 337
831 Problem Formulation 339
832 The Spatial Covariance Matrix 340
833 Bearing Estimation Based on the Spatial Covariance Matrix 342
834 The Spatial Fourth-Order Cumulant Matrix and Bearing
Estimation 346
835 Bearing Estimation with Cross-Bispectrum Beamforming-352
836 MUSIC-Like Method Based on Cumulants 361
8 4 PARAMETER ESTIMATION OF TRANSIENT SIGNALS 366
841 Problem Formulation 366
842 The Third-Order Recursion Equation 367
843 Parameter Estimation Method 367
844 Parameter Estimation with Fourth-Order Moments 370
8 5 DETECTION OF TRANSIENT SIGNALS 371
851 Detection of Transient Signals Using the Bispectrum 373
852 Signal Detection Using Matched Filter Operations 375
Contents
xiii
8 6 SUMMARY 377
REFERENCES , 378
CHAPTER 9 ADAPTIVE FILTERING WITH HIGHER-ORDER
STATISTICS 383
9 1 INTRODUCTION 383
9 2 ADAPTIVE FILTERING WITH SECOND-ORDER STATISTICS 384
921 The Steepest Descent Method 385
922 The LMS Algorithm 387
923 The RLS Algorithm 388
9 3 THE LMF AND RLF ALGORITHM 390
931 The LMF Algorithm 392
932 The RLF Algorithm 396
9 4 ADAPTIVE HR ALGORITHMS BASED ON HOS 397
941 An Adaptive Algorithm for MA Processes
Based on Third-Order Cumulants 397
942 Adaptive Algorithms for ARMA Processes 400
9 5 ADAPTIVE LATTICE LINEAR PREDICTION USING
CUMULANTS 402
9 6 ADAPTIVE MA MODEL ESTIMATION VIA NONCAUSAL
AR APPROXIMATIONS 406
9 7 ADAPTIVE TIME DELAY ESTIMATION 414
9 8 ADAPTIVE BLIND EQUALIZATION ALGORITHMS 418
981 The Bussgang Techniques 422
982 The Polyspectra Algorithms 427
9 9 SUMMARY 441
REFERENCES 443
CHAPTER 10 DETECTION AND CHARACTERIZATION OF
NONLINEARITIES IN TIME SERIES 447
10 1 GENERAL VOLTERRA SYSTEMS 448
10 2 SECOND-ORDER VOLTERRA FILTERS 448
xiv
Contents
10 2 1 Identification Assuming Gaussian Input and Access
to Both Input and Output 449
10 2 2 Identification Assuming a Simple Linear Term and White
Unobservable Input 451
10 2 3 Identification Assuming General Non-Gaussian Input:
Three-Wave Coupling Equation 453
10 3 THE IDENTIFICATION OF A PARTICULAR NONLINEAR
TIME SERIES SYSTEM 455
10 4 QUADRATIC PHASE COUPLING 459
10 4 1 Conventional Techniques for Detection and
Quantification of Quadratic Phase Coupling 461
10 4 2 Parametric Methods for the Detection of
Phase Coupling 465
10 4 3 Time-Domain Approach to Quadratic Phase
Coupling Estimation 476
10 5 CUBIC PHASE COUPLING 482
10 6 SUMMARY 483
REFERENCES 484
CHAPTER 11 TIME-FREQUENCY DISTRIBUTIONS BASED ON
HIGHER-ORDER SPECTRA 487
11 1 INTRODUCTION 487
11 2 WIGNER-VILLE DISTRIBUTION (WD) 488
11 3 COHEN’S GENERAL CLASS OF TIME-FREQUENCY
DISTRIBUTIONS 491
11 3 1 Reduced Interference Distributions 492
11 4 WIGNER HIGHER-ORDER MOMENT SPECTRA:
CONTINUOUS CASE 494
11 4 1 Definition 495
11 4 2 Properties 496
11 4 3 General Class of Time-Frequency Higher-Order Spectra-Based
Distributions 501
11 4 4 Reduced Interference Higher-Order Distribution (RIHOD) 502
Contents xv
11 5 WIGNER POLYSPECTRA: DISCRETE CASE 503
11 5 1 Discrete Time WHOMS (DT-WHOMS) 504
11 5 2 Discrete Frequency WHOMS (DF-WHOMS) 504
11 5 3 Discrete Time and Frequency WHOMS (DTF-WHOMS) 505
11 5 4 Computation of DTF-WHOMS 507
11 5 5 Relation Between the WHOMS and the DTF-WHOMS
After Sampling 508
11 6 APPLICATIONS OF WIGNER HIGHER-ORDER SPECTRA 512
11 7 SUMMARY 520
REFERENCES 520
CHAPTER 12 CURRENT AND FUTURE TRENDS 525
REFERENCES 526 |
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| id | DE-604.BV008272220 |
| illustrated | Illustrated |
| indexdate | 2024-09-07T00:11:26Z |
| institution | BVB |
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| language | English |
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| record_format | marc |
| series2 | Prentice Hall signal processing series |
| spelling | Nikias, Chrysostomos Loizos Verfasser aut Higher-order spectra analysis a nonlinear signal processing framework Chrysostomos L. Nikias ; Athina P. Petropulu Higher order spectra analysis Englewood Cliffs, NJ Prentice-Hall 1993 XXII, 537 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Prentice Hall signal processing series Analise de series temporais larpcal Estatistica aplicada larpcal Processamento e detecao de sinais larpcal Spectroscopie ram Séries chronologiques ram Traitement du signal - Techniques numériques ram Signal processing Statistical methods Spectrum analysis Time-series analysis Signalverarbeitung (DE-588)4054947-1 gnd rswk-swf Spektralanalyse (DE-588)4132368-3 gnd rswk-swf Spektralanalyse (DE-588)4132368-3 s Signalverarbeitung (DE-588)4054947-1 s DE-604 Petropulu, Athina P. Verfasser aut HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005464625&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nikias, Chrysostomos Loizos Petropulu, Athina P. Higher-order spectra analysis a nonlinear signal processing framework Analise de series temporais larpcal Estatistica aplicada larpcal Processamento e detecao de sinais larpcal Spectroscopie ram Séries chronologiques ram Traitement du signal - Techniques numériques ram Signal processing Statistical methods Spectrum analysis Time-series analysis Signalverarbeitung (DE-588)4054947-1 gnd Spektralanalyse (DE-588)4132368-3 gnd |
| subject_GND | (DE-588)4054947-1 (DE-588)4132368-3 |
| title | Higher-order spectra analysis a nonlinear signal processing framework |
| title_alt | Higher order spectra analysis |
| title_auth | Higher-order spectra analysis a nonlinear signal processing framework |
| title_exact_search | Higher-order spectra analysis a nonlinear signal processing framework |
| title_full | Higher-order spectra analysis a nonlinear signal processing framework Chrysostomos L. Nikias ; Athina P. Petropulu |
| title_fullStr | Higher-order spectra analysis a nonlinear signal processing framework Chrysostomos L. Nikias ; Athina P. Petropulu |
| title_full_unstemmed | Higher-order spectra analysis a nonlinear signal processing framework Chrysostomos L. Nikias ; Athina P. Petropulu |
| title_short | Higher-order spectra analysis |
| title_sort | higher order spectra analysis a nonlinear signal processing framework |
| title_sub | a nonlinear signal processing framework |
| topic | Analise de series temporais larpcal Estatistica aplicada larpcal Processamento e detecao de sinais larpcal Spectroscopie ram Séries chronologiques ram Traitement du signal - Techniques numériques ram Signal processing Statistical methods Spectrum analysis Time-series analysis Signalverarbeitung (DE-588)4054947-1 gnd Spektralanalyse (DE-588)4132368-3 gnd |
| topic_facet | Analise de series temporais Estatistica aplicada Processamento e detecao de sinais Spectroscopie Séries chronologiques Traitement du signal - Techniques numériques Signal processing Statistical methods Spectrum analysis Time-series analysis Signalverarbeitung Spektralanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005464625&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nikiaschrysostomosloizos higherorderspectraanalysisanonlinearsignalprocessingframework AT petropuluathinap higherorderspectraanalysisanonlinearsignalprocessingframework AT nikiaschrysostomosloizos higherorderspectraanalysis AT petropuluathinap higherorderspectraanalysis |