Optimal filtering: 2 Spatio-temporal fields
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1999
|
| Series: | Mathematics and its applications
481 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 359 S. |
| ISBN: | 0792357345 |
Staff View
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Record in the Search Index
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| adam_text | IMAGE 1
OPTIMAL FILTERING
VOLUME II: SPATIO-TEMPORAL FIELDS
BY VLADIMIR FOMIN DEPARTMENT OF MATHEMATICS AND MECHANICS, ST PETERSBURG
STATE UNIVERSITY,
ST PETERSBURG, RUSSIA
KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON
IMAGE 2
CONTENTS
PREFACE XI
1 FIELDS AND MEANS OF DESCRIBING T H EM 1
1.1 REGULAER FIELDS 2
1.1.1 PRELIMINARY INFORMATION ON FIELDS 2
1.1.2 FIELDS AS ELEMENTS OF HILBERT SPACE 3
1.1.3 STOCHASTIC FIELDS 6
1.2 GENERALIZED FIELDS 7
1.2.1 COMPLETION OF HILBERT SPACE 8
1.2.2 FIELDS AS GENERALIZED ELEMENTS OF HILBERT SPACE 9
1.3 SPATIO-TEMPORAL FIELDS AND FREQUENCY-WAVE FIELDS 20
1.3.1 SPATIO-TEMPORAL FIELDS 20
1.3.2 FREQUENCY-WAVE FIELDS 22
1.4 STOCHASTIC DISCRETE FIELDS 26
1.4.1 FIELDS ON DISCRETE LATTICES 26
1.4.2 MULTI-VARIABLE DIFFERENCE EQUATIONS 30
1.4.3 CAUCHY PROBLERN FOR REGRESSIVE EQUATION 33
1.5 PROOFS OF LEMMAS AND THEOREMS 36
1.5.1 PROOF OF LEMMA 1.1 36
1.5.2 PROOF OF LEMMA 1.2 36
1.5.3 PROOF OF LEMMA 1.3 37
1.5.4 PROOF OF LEMMA 1.4 38
1.5.5 PROOF OF THEOREM 1.1 38
1.5.6 PROOF OF LEMMA 1.5 40
1.5.7 PROOF OF THEOREM 1.2 40
1.6 BIBLIOGRAPHICAL COMMENTS 41
2 MODELS OF CONTINUOUS FIELDS AND ASSOCIATED PROBLEMS 43
2.1 FIELDS IN ELECTRODYNAMICS 45
2.1.1 INITIAL BOUNDARY VALUE PROBLEM 46
V
IMAGE 3
VI CONTENTS
2.1.2 ELECTROSTATIC BOUNDARY VALUE PROBLEM 57
2.1.3 ELECTRODYNAMICS OF HOLLOW SYSTEMS 70
2.2 ACOUSTIC FIELDS 94
2.2.1 ACOUSTIC WAVES IN THE WORLD S OCEAN 94
2.2.2 ACOUSTIC FIELDS IN CYLINDRICAL WAVEGUIDES 99
2.3 PARAMETRIC VIBRATIONS OF DISTRIBUTED SYSTEMS 120
2.3.1 A GENERAL IDEA OF PARAMETRIC RESONANCE 120
2.3.2 EXAMPLES OF MODELES OF PARAMETRIC VIBRATIONS 125
2.3.3 COLLECTION OF SOME RESULTS ON PARAMETRIC VIBRATIONS . . . 132 2.4
PROOFS OF LEMMAS AND THEOREMS 139
2.4.1 PROOFOF LEMMA 2.1 139
2.4.2 PROOFOF LEMMA 2.2 140
2.4.3 PROOFOF LEMMA 2.3 140
2.4.4 PROOFOF LEMMA 2.4 141
2.4.5 PROOFOF LEMMA 2.5 142
2.4.6 PROOFOF LEMMA 2.6 142
2.4.7 PROOFOF THEOREM 2.1 143
2.4.8 PROOFOF LEMMA 2.7 144
2.4.9 PROOFOF LEMMA 2.8 144
2.4.10 PROOF OF THEOREM 2.2 145
2.4.11 PROOFOF LEMMA 2.9 146
2.4.12 PROOF OF LEMMA 2.10 147
2.4.13 PROOF OF LEMMA 2.11 147
2.4.14 PROOFOF LEMMA 2.12 149
2.4.15 PROOF OF LEMMA 2.13 149
2.4.16 PROOF OF LEMMA 2.14 150
2.4.17 PROOF OF THEOREM 2.3 150
2.4.18 PROOF OF LEMMA 2.15 152
2.4.19 PROOF OF THEOREM 2.5 153
2.4.20 PROOF OF THEOREM 2.6 153
2.4.21 PROOF OF THEOREM 2.7 153
2.5 BIBLIOGRAPHICAL COMMENTS 156
3 FILTERING OF SPATIO-TEMPORAL FIELDS 161
3.1 LINEAR ALTERS AND ANTENNA ARRAYS 161
3.1.1 LINEAR FILTERING OF FIELDS 161
3.1.2 ANTENNA ARRAYS 163
3.1.3 TUNABLE ALTERS WITH NEURON TYPE OF STRUCTURE 170
3.2 SIGNAL OPTIMAL DETECTION 173
3.2.1 BAYES APPROACH TO THE PROBLEM OF DECISION MAKING . . . 173 3.2.2
SIMPLIFICATION OF BAYES DECISION RULE 175
3.2.3 BAYES DECISION RULE FOR GAUSSIAN SIGNALS 180
3.2.4 FACTORIZATION OF THE QUADRATIC FORM OPERATOR 185
3.3 ESTIMATION OF ANGLES OF ARRIVAL OF LOCAL SIGNALS 188
IMAGE 4
CONTENTS VII
3.3.1 SIGNAL TO NOISE MODEL OF SPATIO-TEMPORAL SIGNAL 189
3.3.2 SOLUBILITY OF THE ANGLES OF ARRIVAL PROBLEM . . . 195
3.3.3 SUBSPACE ROTATION APPROACH OF SIGNAL PARAMETER ESTIMATION 203
3.3.4 MOVING ANTENNA ARRAY 206
3.3.5 ADAPTIVE FILTERING 210
3.4 PROOFS OF LEMMAS AND THEOREMS 218
3.4.1 PROOF OF THEOREM 3.1 218
3.4.2 PROOF OF LEMMA 3.1 219
3.5 BIBLIOGRAPHICAL COMMENTS 219
4 OPTIMAL FILTERING OF DISCRETE HOMOGENEOUS FIELDS 221
4.1 OPTIMAL FILTERING OF DISCRETE HOMOGENEOUS FIELDS 221
4.1.1 LINEAR FILTER AND MEAN SQUARE PERFORMANCE CRITERION . . 222 4.1.2
FILTERING PROBLEM (STABILITY AND REALIZABILITY) 223
4.1.3 OPTIMAL FILTERING PROBLEM IN FREQUENCY TERMS 225
4.1.4 OPTIMIZATION OF STATIONARY ALTERS 226
4.1.5 OPTIMIZATION OF STABLE NON-STATIONARY ALTERS 227
4.1.6 OPTIMIZATION OF PHYSICALLY REALIZABLE ALTERS 228
4.2 SYNTHESIS OF OPTIMAL PHYSICALLY REALIZABLE STATIONARY FILTER . . .
229 4.2.1 GENERAL SCHEME 229
4.2.2 EXAMPLE: OPTIMAL FILTERING OF STATIONARY TIME SERIES . . 234 4.3
OPTIMAL PREDICTION OF TWO-DIMENSIONAL REGRESSIVE FIELDS 236
4.3.1 OPTIMAL PREDICTION SCHEME 236
4.3.2 STABLE AUTOREGRESSIVE EQUATION 237
4.3.3 SEPARATION OF RATIONAL FUNCTIONS 238
4.3.4 RECURRENCE REPRESENTATION OF OPTIMAL FILTER 240
4.3.5 STRUCTURE OF OPTIMAL FILTER 240
4.3.6 SPECIAL CASE OF UNSTABLE AUTOREGRESSIVE EQUATION 241
4.4 MULTI-DIMENSIONAL FACTORIZATION AND ITS ATTENDANT PROBLEMS . . 243
4.4.1 FACTORIZATION OF SPECTRAL DENSITY 245
4.4.2 CEPSTRUM IN THE FACTORIZATION PROBLEM 246
4.4.3 FORMATIVE FILTER FOR HOMOGENEOUS FIELD 248
4.5 PROOFS OF LEMMAS AND THEOREMS 250
4.5.1 PROOF OF THEOREM 4.1 250
4.5.2 PROOF OF THEOREM 4.3 251
4.5.3 PROOF OF THEOREM 4.4 252
4.5.4 PROOF OF THEOREM 4.5 253
4.5.5 PROOF OF LEMMA 4.1 253
4.5.6 PROOF OF THEOREM 4.6 255
4.6 BIBLIOGRAPHICAL COMMENTS 258
A APPENDIX: FIELDS IN ELECTRODYNAMICS 259
A.L SELF-CONJUGATE LAPLACE OPERATOR 259
IMAGE 5
V L LL CONTENTS
A.L.L LAPLACE OPERATOR IN INVARIANT SUBSPACE 260
A.1.2 INVARIANT SUBSPACES OF LAPLACE OPERATOR 263
A.1.3 CONTINUOUS SPECTRUM OF LAPLACE OPERATOR 268
A.2 ELECTRODYNAMIC PROBLEM IN TUBE DOMAIN 273
A.2.1 EIGENFIELDS IN TUBE DOMAIN 273
A.2.2 EXAMPLE: OSCILLATIONS IN RECTANGULAR RESONATOR 277
A.2.3 EXAMPLE: RECTANGULAR SEMI-INFINITE WAVEGUIDE 278
A.3 PROOFS OF LEMMAS AND THEOREMS 279
A.3.1 PROOFOF LEMMA A.L 279
A.3.2 PROOFOF LEMMA A.2 279
A.3.3 PROOFOF LEMMA A.3 280
A.3.4 PROOFOF LEMMA A.4 281
A.3.5 PROOF OF LEMMA A.5 282
A.3.6 PROOF OF LEMMA A.6 282
A.3.7 PROOFOF THEOREM A.L 283
A.4 BIBLIOGRAPHICAL COMMENTS 283
B APPENDIX: SPECTRAL ANALYSIS OF TIME SERIES 285
B.L RECONSTRUCTION OF SPECTRAL DENSITIES 286
B.1.1 QUASI-STATIONARY SIGNALS AND THEIR POWER SPECTRA . . .. 286 B.L.2
OPTIMAL ESTIMATION OF POWER SPECTRUM 293
B.2 PADE APPROXIMATION 297
B.2.1 PADE APPROXIMATION OF ANALYTIC FUNCTION 298
B.2.2 PADE APPROXIMATION OF SPECTRAL DENSITY 300
B.3 IDENTIFICATION OF REGRESSIVE EQUATION 302
B.3.1 OPTIMAL PREDICTION 304
B.3.2 ESTIMATION OF COEFFICIENTS OF REGRESSIVE EQUATION 308
B.4 PROOFS OF LEMMAS AND THEOREMS 310
B.4.1 PROOF OF LEMMA B.L 310
B.4.2 PROOF OF THEOREM B.L 311
B.4.3 PROOF OF THEOREM B.2 311
B.4.4 PROOF OF THEOREM B.3 312
B.4.5 PROOFOF LEMMA B.2 312
B.4.6 PROOF OF THEOREM B.4 313
B.4.7 PROOFOF LEMMA B.3 314
B.4.8 PROOF OF LEMMA B.4 315
B.4.9 PROOF OF LEMMA B.5 316
B.4.10 PROOF OF LEMMA B.6 316
B.5 BIBLIOGRAPHICAL COMMENTS 317
C APPENDIX: SPECTRAL ANALYSIS OF DISCRETE HOMOGENEOUS FIELDS 321 C.L
LATTICED CONES AND FUNCTIONS 321
C.L.L LATTICED CONES 321
C.1.2 LATTICED FIELDS 323
/
IMAGE 6
CONTENTS IX
C.2 DISCRETE FIELDS 327
C.2.1 GENERALIZED DISCRETE FIELDS *. . . 327
C.2.2 STOCHASTIC FIELDS 329
C.3 LATTICED CONE ALTERS 333
C.3.1 STAHLE LINEAR ALTERS 333
C.3.2 MULTI-VARIATE ANALOG OF PADE APPROXIMATION 337
C.4 PROOFS OF LEMMAS AND THEOREMS 341
C.4.1 PROOFOF LEMMA C.L 341
C.4.2 PROOFOF THEOREM C.L 342
C.4.3 PROOFOF LEMMA C.2 342
C.4.4 PROOFOF THEOREM C.2 343
C.5 BIBLIOGRAPHICAL COMMENTS 343
REFERENCES 345
NOTATION 353
INDEX 357
|
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| spelling | Fomin, Vladimir N. 1937-2000 Verfasser (DE-588)131358073 aut Optimal filtering 2 Spatio-temporal fields Vladimir Fomin Dordrecht [u.a.] Kluwer 1999 XII, 359 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 481 Mathematics and its applications ... (DE-604)BV012513823 2 Mathematics and its applications 481 (DE-604)BV008163334 481 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009117468&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fomin, Vladimir N. 1937-2000 Optimal filtering Mathematics and its applications |
| title | Optimal filtering |
| title_auth | Optimal filtering |
| title_exact_search | Optimal filtering |
| title_full | Optimal filtering 2 Spatio-temporal fields Vladimir Fomin |
| title_fullStr | Optimal filtering 2 Spatio-temporal fields Vladimir Fomin |
| title_full_unstemmed | Optimal filtering 2 Spatio-temporal fields Vladimir Fomin |
| title_short | Optimal filtering |
| title_sort | optimal filtering spatio temporal fields |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009117468&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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