Complex valued nonlinear adaptive filters: noncircularity, widely linear, and neural models
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester
Wiley
2009
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Adaptive and Learning Systems for Signal Processing, Communications and Control
|
| Schlagworte: | |
| Online-Zugang: | Cover Inhaltsverzeichnis |
| Beschreibung: | XVIII, 324 S. graph. Darst. |
| ISBN: | 9780470066355 |
Internformat
MARC
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| 245 | 1 | 0 | |a Complex valued nonlinear adaptive filters |b noncircularity, widely linear, and neural models |c Danilo P. Mandic ; Vanessa Su Lee Goh |
| 250 | |a 1. publ. | ||
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| 490 | 0 | |a Adaptive and Learning Systems for Signal Processing, Communications and Control | |
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| 650 | 7 | |a Traitement adaptatif du signal |2 ram | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Functions of complex variables | |
| 650 | 4 | |a Adaptive filters / Mathematical models | |
| 650 | 4 | |a Filters (Mathematics) | |
| 650 | 4 | |a Nonlinear theories | |
| 650 | 4 | |a Neural networks (Computer science) | |
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Datensatz im Suchindex
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| adam_text | COMPLEX VALUED NONLINEAR ADAPTIVE FILTERS NONCIRCULARITY, WIDELY LINEAR
AND NEURAL MODELS DANILO P. MANDIC IMPERIAL COLLEGE LONDON, UK VANESSA
SU LEE GOH SHELL EP, EUROPE WILEY A JOHN WILEY AND SONS, LTD,
PUBLICATION CONTENTS PREFACE XIII ACKNOWLEDGEMENTS XVII 1 THE MAGIC OF
COMPLEX NUMBERS 1 1.1 HISTORY OF COMPLEX NUMBERS 2 1.1.1 HYPERCOMPLEX
NUMBERS 7 1.2 HISTORY OF MATHEMATICAL NOTATION 8 1.3 DEVELOPMENT OF
COMPLEX VALUED ADAPTIVE SIGNAL PROCESSING 9 2 WHY SIGNAL PROCESSING IN
THE COMPLEX DOMAIN? 13 2.1 SOME EXAMPLES OF COMPLEX VALUED SIGNAL
PROCESSING 13 2.1.1 DUALITY BETWEEN SIGNAL REPRESENTATIONS IN * AND * 18
2.2 MODELLING IN * IS NOT ONLY CONVENIENT BUT ALSO NATURAL 19 2.3 WHY
COMPLEX MODELLING OF REAL VALUED PROCESSES? 20 2.3.1 PHASE INFORMATION
IN IMAGING 20 2.3.2 MODELLING OF DIRECTIONAL PROCESSES 22 2.4 EXPLOITING
THE PHASE INFORMATION 23 2.4.1 SYNCHRONISATION OF REAL VALUED PROCESSES
24 2.4.2 ADAPTIVE FILTERING BY INCORPORATING PHASE INFORMATION 25 2.5
OTHER APPLICATIONS OF COMPLEX DOMAIN PROCESSING OF REAL VALUED SIGNALS
26 2.6 ADDITIONAL BENEFITS OF COMPLEX DOMAIN PROCESSING 29 3 ADAPTIVE
FILTERING ARCHITECTURES 33 3.1 LINEAR AND NONLINEAR STOCHASTIC MODELS 34
3.2 LINEAR AND NONLINEAR ADAPTIVE FILTERING ARCHITECTURES 35 3.2.1
FEEDFORWARD NEURAL NETWORKS 36 3.2.2 RECURRENT NEURAL NETWORKS 37 3.2.3
NEURAL NETWORKS AND POLYNOMIAL FILTERS 38 3.3 STATE SPACE REPRESENTATION
AND CANONICAL FORMS 39 VIII CONTENTS 4 COMPLEX NONLINEAR ACTIVATION
FUNCTIONS 43 4.1 PROPERTIES OF COMPLEX FUNCTIONS 43 4.1.1 SINGULARITIES
OF COMPLEX FUNCTIONS 45 4.2 UNIVERSAL FUNCTION APPROXIMATION 46 4.2.1
UNIVERSAL APPROXIMATION IN R 47 4.3 NONLINEAR ACTIVATION FUNCTIONS FOR
COMPLEX NEURAL NETWORKS 48 4.3.1 SPLIT-COMPLEX APPROACH 49 4.3.2 FULLY
COMPLEX NONLINEAR ACTIVATION FUNCTIONS 51 4.4 GENERALISED SPLITTING
ACTIVATION FUNCTIONS (GSAF) 53 4.4.1 THE CLIFFORD NEURON 53 4.5 SUMMARY:
CHOICE OF THE COMPLEX ACTIVATION FUNCTION 54 5 ELEMENTS OF CR CALCULUS
55 5.1 CONTINUOUS COMPLEX FUNCTIONS 56 5.2 THE CAUCHY-RIEMANN EQUATIONS
56 5.3 GENERALISED DERIVATIVES OF FUNCTIONS OF COMPLEX VARIABLE 57 5.3.1
CR CALCULUS 59 5.3.2 LINK BETWEEN R- AND C-DERIVATIVES 60 5.4
CR-DERIVATIVES OF COST FUNCTIONS 62 5.4.1 THE COMPLEX GRADIENT 62 5.4.2
THE COMPLEX HESSIAN 64 5.4.3 THE COMPLEX JACOBIAN AND COMPLEX
DIFFERENTIAL 64 5.4.4 GRADIENT OF A COST FUNCTION 65 6 COMPLEX VALUED
ADAPTIVE FILTERS 69 6.1 ADAPTIVE FILTERING CONFIGURATIONS 70 6.2 THE
COMPLEX LEAST MEAN SQUARE ALGORITHM 73 6.2.1 CONVERGENCE OF THE CLMS
ALGORITHM 75 6.3 NONLINEAR FEEDFORWARD COMPLEX ADAPTIVE FILTERS 80 6.3.1
FULLY COMPLEX NONLINEAR ADAPTIVE FILTERS 80 6.3.2 DERIVATION OF CNGD
USING CR CALCULUS 82 6.3.3 SPLIT-COMPLEX APPROACH 83 6.3.4 DUAL
UNIVARIATE ADAPTIVE FILTERING APPROACH (DUAF) 84 6.4 NORMALISATION OF
LEARNING ALGORITHMS 85 6.5 PERFORMANCE OF FEEDFORWARD NONLINEAR ADAPTIVE
FILTERS 87 6.6 SUMMARY: CHOICE OF A NONLINEAR ADAPTIVE FILTER 89 7
ADAPTIVE FILTERS WITH FEEDBACK 91 7.1 TRAINING OF IIR ADAPTIVE FILTERS
92 7.1.1 COEFFICIENT UPDATE FOR LINEAR ADAPTIVE IIR FILTERS 93 7.1.2
TRAINING OF IIR FILTERS WITH REDUCED COMPUTATIONAL COMPLEXITY 96
CONTENTS IX 7.2 NONLINEAR ADAPTIVE HR FILTERS: RECURRENT PERCEPTRON 97
7.3 TRAINING OF RECURRENT NEURAL NETWORKS 99 7.3.1 OTHER LEARNING
ALGORITHMS AND COMPUTATIONAL COMPLEXITY 102 7.4 SIMULATION EXAMPLES 102
8 FILTERS WITH AN ADAPTIVE STEPSIZE 107 8.1 BENVENISTE TYPE VARIABLE
STEPSIZE ALGORITHMS 108 8.2 COMPLEX VALUED GNGD ALGORITHMS 110 8.2.1
COMPLEX GNGD FOR NONLINEAR FILTERS (CFANNGD) 112 8.3 SIMULATION EXAMPLES
113 9 FILTERS WITH AN ADAPTIVE AMPLITUDE OF NONLINEARITY 119 9.1
DYNAMICAL RANGE REDUCTION 119 9.2 FIR ADAPTIVE FILTERS WITH AN ADAPTIVE
NONLINEARITY 121 9.3 RECURRENT NEURAL NETWORKS WITH TRAINABLE AMPLITUDE
OF ACTIVATION FUNCTIONS 122 9.4 SIMULATION RESULTS 124 10 DATA-REUSING
ALGORITHMS FOR COMPLEX VALUED ADAPTIVE FILTERS 129 10.1 THE DATA-REUSING
COMPLEX VALUED LEAST MEAN SQUARE (DRCLMS) ALGORITHM 129 10.2
DATA-REUSING COMPLEX NONLINEAR ADAPTIVE FILTERS 131 10.2.1 CONVERGENCE
ANALYSIS 132 10.3 DATA-REUSING ALGORITHMS FOR COMPLEX RNNS 134 11
COMPLEX MAPPINGS AND MOEBIUS TRANSFORMATIONS 137 11.1 MATRIX
REPRESENTATION OF A COMPLEX NUMBER 137 11.2 THE MOEBIUS TRANSFORMATION
140 11.3 ACTIVATION FUNCTIONS AND MOEBIUS TRANSFORMATIONS 142 11.4
ALL-PASS SYSTEMS AS MOEBIUS TRANSFORMATIONS 146 11.5 FRACTIONAL DELAY
FILTERS 147 12 AUGMENTED COMPLEX STATISTICS 151 12.1 COMPLEX RANDOM
VARIABLES (CRV) 152 12.1.1 COMPLEX CIRCULARITY 153 12.1.2 THE
MULTIVARIATE COMPLEX NORMAL DISTRIBUTION 154 12.1.3 MOMENTS OF COMPLEX
RANDOM VARIABLES (CRV) 157 12.2 COMPLEX CIRCULAR RANDOM VARIABLES 158
12.3 COMPLEX SIGNALS 159 12.3.1 WIDE SENSE STATIONARITY,
MULTICORRELATIONS, AND MULTISPECTRA 160 12.3.2 STRICT CIRCULARITY AND
HIGHER-ORDER STATISTICS 161 12.4 SECOND-ORDER CHARACTERISATION OF
COMPLEX SIGNALS 161 12.4.1 AUGMENTED STATISTICS OF COMPLEX SIGNALS 161
12.4.2 SECOND-ORDER COMPLEX CIRCULARITY 164 X CONTENTS 13 WIDELY LINEAR
ESTIMATION AND AUGMENTED CLMS (ACLMS) 169 13.1 MINIMUM MEAN SQUARE ERROR
(MMSE) ESTIMATION IN * 169 13.1.1 WIDELY LINEAR MODELLING IN * 171 13.2
COMPLEX WHITE NOISE 172 13.3 AUTOREGRESSIVE MODELLING IN * 173 13.3.1
WIDELY LINEAR AUTOREGRESSIVE MODELLING IN * 174 13.3.2 QUANTIFYING
BENEFITS OF WIDELY LINEAR ESTIMATION 174 13.4 THE AUGMENTED COMPLEX LMS
(ACLMS) ALGORITHM 175 13.5 ADAPTIVE PREDICTION BASED ON ACLMS 178 13.5.1
WIND FORECASTING USING AUGMENTED STATISTICS 180 14 DUALITY BETWEEN
COMPLEX VALUED AND REAL VALUED FILTERS 183 14.1 A DUAL CHANNEL REAL
VALUED ADAPTIVE FILTER 184 14.2 DUALITY BETWEEN REAL AND COMPLEX VALUED
FILTERS 186 14.2.1 OPERATION OF STANDARD COMPLEX ADAPTIVE FILTERS 186
14.2.2 OPERATION OF WIDELY LINEAR COMPLEX FILTERS 187 14.3 SIMULATIONS
188 15 WIDELY LINEAR FILTERS WITH FEEDBACK 191 15.1 THE WIDELY LINEAR
ARMA (WL-ARMA) MODEL 192 15.2 WIDELY LINEAR ADAPTIVE FILTERS WITH
FEEDBACK 192 15.2.1 WIDELY LINEAR ADAPTIVE IIR FILTERS 195 15.2.2
AUGMENTED RECURRENT PERCEPTRON LEARNING RULE 196 15.3 THE AUGMENTED
COMPLEX VALUED RTRL (ACRTRL) ALGORITHM 197 15.4 THE AUGMENTED KAIMAN
FILTER ALGORITHM FOR RNNS 198 15.4.1 EKF BASED TRAINING OF COMPLEX RNNS
200 15.5 AUGMENTED COMPLEX UNSCENTED KAIMAN FILTER (ACUKF) 200 15.5.1
STATE SPACE EQUATIONS FOR THE COMPLEX UNSCENTED KAIMAN FILTER 201 15.5.2
ACUKF BASED TRAINING OF COMPLEX RNNS 202 15.6 SIMULATION EXAMPLES 203 16
COLLABORATIVE ADAPTIVE FILTERING 207 16.1 PARAMETRIC SIGNAL MODALITY
CHARACTERISATION 207 16.2 STANDARD HYBRID FILTERING IN R 209 16.3
TRACKING THE LINEAR/NONLINEAR NATURE OF COMPLEX VALUED SIGNALS 210
16.3.1 SIGNAL MODALITY CHARACTERISATION IN * 211 16.4 SPLIT VS FULLY
COMPLEX SIGNAL NATURES 214 16.5 ONLINE ASSESSMENT OF THE NATURE OF WIND
SIGNAL 216 16.5.1 EFFECTS OF AVERAGING ON SIGNAL NONLINEARITY 216 16.6
COLLABORATIVE FILTERS FOR GENERAL COMPLEX SIGNALS 217 16.6.1 HYBRID
FILTERS FOR NONCIRCULAR SIGNALS 218 16.6.2 ONLINE TEST FOR COMPLEX
CIRCULARITY 220 CONTENTS XI 17 ADAPTIVE FILTERING BASED ON EMD 221 17.1
THE EMPIRICAL MODE DECOMPOSITION ALGORITHM 222 17.1.1 EMPIRICAL MODE
DECOMPOSITION AS A FIXED POINT ITERATION 223 17.1.2 APPLICATIONS OF REAL
VALUED EMD 224 17.1.3 UNIQUENESS OF THE DECOMPOSITION 225 17.2 COMPLEX
EXTENSIONS OF EMPIRICAL MODE DECOMPOSITION 226 17.2.1 COMPLEX EMPIRICAL
MODE DECOMPOSITION 227 17.2.2 ROTATION INVARIANT EMPIRICAL MODE
DECOMPOSITION (RIEMD) 228 17.2.3 BIVARIATE EMPIRICAL MODE DECOMPOSITION
(BEMD) 228 17.3 ADDRESSING THE PROBLEM OF UNIQUENESS 230 17.4
APPLICATIONS OF COMPLEX EXTENSIONS OF EMD 230 18 VALIDATION OF COMPLEX
REPRESENTATIONS - IS THIS WORTHWHILE? 233 18.1 SIGNAL MODALITY
CHARACTERISATION IN * 234 18.1.1 SURROGATE DATA METHODS 235 18.1.2 TEST
STATISTICS: THE DVV METHOD 237 18.2 TESTING FOR THE VALIDITY OF COMPLEX
REPRESENTATION 239 18.2.1 COMPLEX DELAY VECTOR VARIANCE METHOD (CDVV)
240 18.3 QUANTIFYING BENEFITS OF COMPLEX VALUED REPRESENTATION 243
18.3.1 PROS AND CONS OF THE COMPLEX DVV METHOD 244 APPENDIX A: SOME
DISTINCTIVE PROPERTIES OF CALCULUS IN * 245 APPENDIX B: LIOUVILLE S
THEOREM 251 APPENDIX C: HYPERCOMPLEX AND CLIFFORD ALGEBRAS 253 C. 1
DEFINITIONS OF ALGEBRAIC NOTIONS OF GROUP, RING AND FIELD 253 C.2
DEFINITION OF A VECTOR SPACE 254 C.3 HIGHER DIMENSION ALGEBRAS 254 C.4
THE ALGEBRA OF QUATERNIONS 255 C.5 CLIFFORD ALGEBRAS 256 APPENDIX D:
REAL VALUED ACTIVATION FUNCTIONS 257 D.L LOGISTIC SIGMOID ACTIVATION
FUNCTION 257 D.2 HYPERBOLIC TANGENT ACTIVATION FUNCTION 258 APPENDIX E:
ELEMENTARY TRANSCENDENTAL FUNCTIONS (ETF) 259 APPENDIX F: THE * NOTATION
AND STANDARD VECTOR AND MATRIX DIFFERENTIATION 263 F.L THE * NOTATION
263 F.2 STANDARD VECTOR AND MATRIX DIFFERENTIATION 263 XII CONTENTS
APPENDIX G: NOTIONS FROM LEARNING THEORY 265 G. 1 TYPES OF LEARNING 266
G.2 THE BIAS-VARIANCE DILEMMA 266 G.3 RECURSIVE AND ITERATIVE GRADIENT
ESTIMATION TECHNIQUES 267 G.4 TRANSFORMATION OF INPUT DATA 267 APPENDIX
H: NOTIONS FROM APPROXIMATION THEORY 269 APPENDIX I: TERMINOLOGY USED IN
THE FIELD OF NEURAL NETWORKS 273 APPENDIX J: COMPLEX VALUED PIPELINED
RECURRENT NEURAL NETWORK (CPRNN) 275 J.L THE COMPLEX RTRL ALGORITHM
(CRTRL) FOR CPRNN 275 J. 1.1 LINEAR SUBSECTION WITHIN THE PRNN 277
APPENDIX K: GRADIENT ADAPTIVE STEP SIZE (GASS) ALGORITHMS IN R 279 K.L
GRADIENT ADAPTIVE STEPSIZE ALGORITHMS BASED ON *//*/* 280 K.2 VARIABLE
STEPSIZE ALGORITHMS BASED ON DJ/DE 281 APPENDIX L: DERIVATION OF PARTIAL
DERIVATIVES FROM CHAPTER 8 283 L.L DERIVATION OF DE(K)/DW N (K) 283 L.2
DERIVATION OF ***(*)/**(* - 1) 284 L.3 DERIVATION OF DW(K)/DS(K - 1) 286
APPENDIX M: A POSTERIORI LEARNING 287 M. 1 A POSTERIORI STRATEGIES IN
ADAPTIVE LEARNING 288 APPENDIX N: NOTIONS FROM STABILITY THEORY 291
APPENDIX O: LINEAR RELAXATION 293 O.L VECTOR AND MATRIX NORMS 293 0.2
RELAXATION IN LINEAR SYSTEMS 294 0.2.1 CONVERGENCE IN THE NORM OR STATE
SPACE? 297 APPENDIX P: CONTRACTION MAPPINGS, FIXED POINT ITERATION AND
FRACTALS 299 P. 1 HISTORICAL PERSPECTIVE 303 P.2 MORE ON CONVERGENCE:
MODIFIED CONTRACTION MAPPING 305 P.3 FRACTALS AND MANDELBROT SET 308
REFERENCES 309 INDEX 321
|
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| discipline | Elektrotechnik Elektrotechnik / Elektronik / Nachrichtentechnik |
| edition | 1. publ. |
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| id | DE-604.BV035636642 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:42:08Z |
| institution | BVB |
| isbn | 9780470066355 |
| language | English |
| lccn | 2009001965 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017691494 |
| oclc_num | 246887497 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | XVIII, 324 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Wiley |
| record_format | marc |
| series2 | Adaptive and Learning Systems for Signal Processing, Communications and Control |
| spelling | Mandic, Danilo P. Verfasser aut Complex valued nonlinear adaptive filters noncircularity, widely linear, and neural models Danilo P. Mandic ; Vanessa Su Lee Goh 1. publ. Chichester Wiley 2009 XVIII, 324 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Adaptive and Learning Systems for Signal Processing, Communications and Control Filtres adaptatifs ram Traitement adaptatif du signal ram Mathematisches Modell Functions of complex variables Adaptive filters / Mathematical models Filters (Mathematics) Nonlinear theories Neural networks (Computer science) Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Adaptives Filter (DE-588)4141377-5 gnd rswk-swf Digitale Signalverarbeitung (DE-588)4113314-6 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Digitale Signalverarbeitung (DE-588)4113314-6 s Adaptives Filter (DE-588)4141377-5 s Mathematisches Modell (DE-588)4114528-8 s Funktionentheorie (DE-588)4018935-1 s Mehrere Variable (DE-588)4277015-4 s DE-604 Goh, Vanessa Su Lee Verfasser aut DE-576;wiley image/jpeg http://swbplus.bsz-bw.de/bsz306347075cov.htm 20090507203435 Cover GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017691494&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mandic, Danilo P. Goh, Vanessa Su Lee Complex valued nonlinear adaptive filters noncircularity, widely linear, and neural models Filtres adaptatifs ram Traitement adaptatif du signal ram Mathematisches Modell Functions of complex variables Adaptive filters / Mathematical models Filters (Mathematics) Nonlinear theories Neural networks (Computer science) Mathematisches Modell (DE-588)4114528-8 gnd Mehrere Variable (DE-588)4277015-4 gnd Adaptives Filter (DE-588)4141377-5 gnd Digitale Signalverarbeitung (DE-588)4113314-6 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4277015-4 (DE-588)4141377-5 (DE-588)4113314-6 (DE-588)4018935-1 |
| title | Complex valued nonlinear adaptive filters noncircularity, widely linear, and neural models |
| title_auth | Complex valued nonlinear adaptive filters noncircularity, widely linear, and neural models |
| title_exact_search | Complex valued nonlinear adaptive filters noncircularity, widely linear, and neural models |
| title_full | Complex valued nonlinear adaptive filters noncircularity, widely linear, and neural models Danilo P. Mandic ; Vanessa Su Lee Goh |
| title_fullStr | Complex valued nonlinear adaptive filters noncircularity, widely linear, and neural models Danilo P. Mandic ; Vanessa Su Lee Goh |
| title_full_unstemmed | Complex valued nonlinear adaptive filters noncircularity, widely linear, and neural models Danilo P. Mandic ; Vanessa Su Lee Goh |
| title_short | Complex valued nonlinear adaptive filters |
| title_sort | complex valued nonlinear adaptive filters noncircularity widely linear and neural models |
| title_sub | noncircularity, widely linear, and neural models |
| topic | Filtres adaptatifs ram Traitement adaptatif du signal ram Mathematisches Modell Functions of complex variables Adaptive filters / Mathematical models Filters (Mathematics) Nonlinear theories Neural networks (Computer science) Mathematisches Modell (DE-588)4114528-8 gnd Mehrere Variable (DE-588)4277015-4 gnd Adaptives Filter (DE-588)4141377-5 gnd Digitale Signalverarbeitung (DE-588)4113314-6 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Filtres adaptatifs Traitement adaptatif du signal Mathematisches Modell Functions of complex variables Adaptive filters / Mathematical models Filters (Mathematics) Nonlinear theories Neural networks (Computer science) Mehrere Variable Adaptives Filter Digitale Signalverarbeitung Funktionentheorie |
| url | http://swbplus.bsz-bw.de/bsz306347075cov.htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017691494&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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