Fundamentals of wavelets: theory, algorithms, and applications
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
New York [u.a.]
Wiley
1999
|
| Schriftenreihe: | Wiley series in microwave and optical engineering
A Wiley-Interscience publication |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 306 S. Ill., graph. Darst. |
| ISBN: | 0471197483 |
Internformat
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| 245 | 1 | 0 | |a Fundamentals of wavelets |b theory, algorithms, and applications |c Jaideva C. Goswami ; Andrew K. Chan |
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Datensatz im Suchindex
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| adam_text | FUNDAMENTALS OF WAVELETS THEORY, ALGORITHMS, AND APPLICATIONS JAIDEVA C.
GOSWAMI ANDREW K. CHAN TEXAS A&M UNIVERSITY F A WILEY-INTERSCIENCE
PUBLICATION JOHN WILEY & SONS, INC NEW YORK / CHICHESTER / WEINHEIM /
BRISBANE / SINGAPORE / TORONTO CONTENTS PREFACE XV 1 WHAT THIS BOOK IS
ABOUT 1 2 MATHEMATICAL PRELIMINARIES 5 2.1 LINEAR SPACES 5 2.2 VECTORS
AND VECTOR SPACES 7 2.3 BASIS FUNCTIONS 9 2.3.1 ORTHOGONALITY AND
BIORTHOGONALITY 10 2.4 LOCAL BASIS AND RIESZ BASIS 13 2.5 DISCRETE
LINEAR NORMED SPACE 15 2.6 APPROXIMATION BY ORTHOGONAL PROJECTION 16 2.7
MATRIX ALGEBRA AND LINEAR TRANSFORMATION 18 2.7.1 ELEMENTS OF MATRIX
ALGEBRA 18 2.7.2 EIGENMATRIX 19 2.7.3 LINEAR TRANSFORMATION 20 2.7.4
CHANGE OF BASIS 21 2.7.5 HERMITIAN MATRIX, UNITARY MATRIX, AND
ORTHOGONAL TRANSFORMATION 22 2.8 DIGITAL SIGNALS 23 2.8.1 SAMPLING OF
SIGNAL 23 2.8.2 LINEAR SHIFT-INVARIANT SYSTEMS 24 2.8.3 CONVOLUTION 24
VII VIII CONTENTS 2.8.4 Z-TRANSFORM 25 2.8.5 REGION OF CONVERGENCE 26
2.8.6 INVERSE Z-TRANSFORM 28 2.9 EXERCISES 29 REFERENCES 30 3 FOURIER
ANALYSIS 31 3.1 FOURIER SERIES 31 3.2 EXAMPLES 32 3.2.1 RECTIFIED SINE
WAVE 32 3.2.2 COMB FUNCTION AND THE FOURIER SERIES KERNEL KN (T) 33 3.3
FOURIER TRANSFORM 35 3.4 PROPERTIES OF THE FOURIER TRANSFORM 37 3.4.1
LINEARITY 37 3.4.2 TIME SHIFTING AND TIME SCALING 38 3.4.3 FREQUENCY
SHIFTING AND FREQUENCY SCALING 38 3.4.4 MOMENTS 38 3.4.5 CONVOLUTION 39
3.4.6 PARSEVAL S THEOREM 40 3.5 EXAMPLES OF THE FOURIER TRANSFORM 40
3.5.1 RECTANGULAR PULSE 41 3.5.2 TRIANGULAR PULSE 41 3.5.3 GAUSSIAN
FUNCTION 42 3.6 POISSON S SUM 43 3.6.1 PARTITION OF UNITY 45 3.7
SAMPLING THEOREM 46 3.8 PARTIAL SUM AND THE GIBBS PHENOMENON 49 3.9
FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS 50 3.9.1 DISCRETE FOURIER
BASIS AND DISCRETE FOURIER SERIES 50 3.9.2 DISCRETE-TIME FOURIER
TRANSFORM 52 3.10 DISCRETE FOURIER TRANSFORM 54 3.11 EXERCISES 55
REFERENCES 56 CONTENTS IX 4 TIME-FREQUENCY ANALYSIS 57 4.1 WINDOW
FUNCTION 58 4.2 SHORT-TIME FOURIER TRANSFORM 60 4.2.1 INVERSION FORMULA
61 4.2.2 GABOR TRANSFORM 61 4.2.3 TIME*FREQUENCY WINDOW 62 4.2.4
PROPERTIES OF STFT 62 4.3 DISCRETE SHORT-TIME FOURIER TRANSFORM 64 4.3.1
EXAMPLES OF STFT 64 4.4 DISCRETE GABOR REPRESENTATION 65 4.5 CONTINUOUS
WAVELET TRANSFORM 67 4.5.1 INVERSE WAVELET TRANSFORM 69 4.5.2
TIME-FREQUENCY WINDOW 70 4.6 DISCRETE WAVELET TRANSFORM 72 4.7 WAVELET
SERIES 73 4.8 INTERPRETATIONS OF THE TIME-FREQUENCY PLOT 74 4.9
WIGNER-VILLE DISTRIBUTION 76 4.10 PROPERTIES OF THE WIGNER-VILLE
DISTRIBUTION 80 4.10.1 A REAL QUANTITY 80 4.10.2 MARGINAL PROPERTIES 80
4.10.3 CORRELATION FUNCTION 81 4.11 QUADRATIC SUPERPOSITION PRINCIPLE 81
4.12 AMBIGUITY FUNCTION 83 4.13 EXERCISES 84 4.14 COMPUTER PROGRAMS 85
4.14.1 SHORT-TIME FOURIER TRANSFORM 85 4.14.2 WIGNER-VILLE DISTRIBUTION
86 REFERENCES 88 5 MULTIRESOLUTION ANALYSIS 89 5.1 MULTIRESOLUTION
SPACES 89 5.2 ORTHOGONAL, BIORTHOGONAL, AND SEMIORTHOGONAL DECOMPOSITION
92 5.3 TWO-SCALE RELATIONS 96 5.4 DECOMPOSITION RELATION 97 K CONTENTS
5.5 SPLINE FUNCTIONS 98 5.5.1 PROPERTIES OF SPLINES 102 5.6 MAPPING A
FUNCTION INTO MRA SPACE 103 5.7 EXERCISES 104 5.8 COMPUTER PROGRAMS 106
5.8.1 5-SPLINES 106 REFERENCES 107 6 CONSTRUCTION OF WAVELETS 108 6.1
NECESSARY INGREDIENTS FOR WAVELET CONSTRUCTION 109 6.1.1 RELATIONSHIP
BETWEEN TWO-SCALE SEQUENCES 109 6.1.2 RELATIONSHIP BETWEEN
RECONSTRUCTION AND DECOMPOSITION SEQUENCES 110 6.2 CONSTRUCTION OF
SEMIORTHOGONAL SPLINE WAVELETS 112 6.2.1 EXPRESSION FOR {G 0 [K]} 113
6.3 CONSTRUCTION OF ORTHONORMAL WAVELETS 114 6.4 ORTHONORMAL SCALING
FUNCTIONS 118 6.4.1 SHANNON SCALING FUNCTION 118 6.4.2 MEYER SCALING
FUNCTION 119 6.4.3 BATTLE-LEMARIE SCALING FUNCTION 123 6.4.4 DAUBECHIES
SCALING FUNCTION 125 6.5 CONSTRUCTION OF BIORTHOGONAL WAVELETS 129 6.6
GRAPHICAL DISPLAY OF WAVELETS 132 6.6.1 ITERATION METHOD 132 6.6.2
SPECTRAL METHOD 132 6.6.3 EIGENVALUE METHOD 134 6.7 EXERCISES 134 6.8
COMPUTER PROGRAMS 138 6.8.1 DAUBECHIES WAVELET 138 6.8.2 ITERATION
METHOD 139 REFERENCES 139 7 DISCRETE WAVELET TRANSFORM AND FILTER BANK
ALGORITHMS 141 7.1 DECIMATION AND INTERPOLATION 141 7.1.1 DECIMATION 142
CONTENTS XI 7.1.2 INTERPOLATION 144 7.1.3 CONVOLUTION FOLLOWED BY
DECIMATION 147 7.1.4 INTERPOLATION FOLLOWED BY CONVOLUTION 147 7.2
SIGNAL REPRESENTATION IN THE APPROXIMATION SUBSPACE 148 7.3 WAVELET
DECOMPOSITION ALGORITHM 149 7.4 RECONSTRUCTION ALGORITHM 153 7.5 CHANGE
OF BASES 154 7.6 SIGNAL RECONSTRUCTION IN SEMIORTHOGONAL SUBSPACES 156
7.6.1 CHANGE OF BASIS FOR SPLINE FUNCTIONS 157 7.6.2 CHANGE OF BASIS FOR
SPLINE WAVELETS 160 7.7 EXAMPLES 163 7.8 TWO-CHANNEL PERFECT
RECONSTRUCTION FILTER BANK 165 7.8.1 SPECTRAL-DOMAIN ANALYSIS OF A
TWO-CHANNEL PR FILTER BANK 168 7.8.2 TIME-DOMAIN ANALYSIS 176 7.9
POLYPHASE REPRESENTATION FOR FILTER BANKS 180 7.9.1 SIGNAL
REPRESENTATION IN THE POLYPHASE DOMAIN 180 7.9.2 FILTER BANK IN THE
POLYPHASE DOMAIN 181 7.10 COMMENTS ON DWT AND PR FILTER BANKS 182 7.11
EXERCISES 183 7.12 COMPUTER PROGRAMS 184 7.12.1 ALGORITHMS 184
REFERENCES 186 8 FAST INTEGRAL TRANSFORM AND APPLICATIONS 187 8.1 FINER
TIME RESOLUTION 188 8.2 FINER SCALE RESOLUTION 190 8.3 FUNCTION MAPPING
INTO THE INTEROCTAVE APPROXIMATION SUBSPACES 194 8.4 EXAMPLES 196 8.4.1
IWT OF A LINEAR FUNCTION 197 8.4.2 CRACK DETECTION 202 8.4.3
DECOMPOSITION OF SIGNALS WITH NONOCTAVE FREQUENCY COMPONENTS 203 8.4.4
PERTURBED SINUSOIDAL SIGNAL 203 8.4.5 CHIRP SIGNAL 204 XII CONTENTS
8.4.6 MUSIC SIGNAL WITH NOISE 204 8.4.7 DISPERSIVE NATURE OF THE
WAVEGUIDE MODE 205 REFERENCES 209 9 DIGITAL SIGNAL PROCESSING
APPLICATIONS 210 9.1 WAVELET PACKETS 211 9.2 WAVELET PACKET ALGORITHMS
212 9.3 THRESHOLDING 214 9.3.1 HARD THRESHOLDING 216 9.3.2 SOFT
THRESHOLDING 217 9.3.3 PERCENTAGE THRESHOLDING 218 9.3.4 IMPLEMENTATION
218 9.4 INTERFERENCE SUPPRESSION 219 9.5 FAULTY BEARING SIGNATURE
IDENTIFICATION 221 9.5.1 PATTERN RECOGNITION OF ACOUSTIC SIGNALS 221
9.5.2 WAVELETS, WAVELET PACKETS, AND FFT FEATURES 226 9.6
TWO-DIMENSIONAL WAVELETS AND WAVELET PACKETS 228 9.6.1 TWO-DIMENSIONAL
WAVELETS 228 9.6.2 TWO-DIMENSIONAL WAVELET PACKETS 231 9.7 WAVELET AND
WAVELET PACKET ALGORITHMS FOR TWO-DIMENSIONAL SIGNALS 233 9.7.1
TWO-DIMENSIONAL WAVELET ALGORITHM 233 9.7.2 WAVELET PACKET ALGORITHM 234
9.8 IMAGE COMPRESSION 235 9.8.1 IMAGE CODING 235 9.8.2 WAVELET TREE
CODER 236 9.8.3 EZWCODE 238 9.8.4 EZW EXAMPLE 239 9.8.5 SPATIAL-ORIENTED
TREE 242 9.8.6 GENERALIZED SELF-SIMILARITY TREE 244 9.9
MICROCALCIFICATION CLUSTER DETECTION 244 9.9.1 CAD ALGORITHM STRUCTURE
244 9.9.2 PARTITIONING OF IMAGE AND NONLINEAR CONTRAST ENHANCEMENT 245
9.9.3 WAVELET DECOMPOSITION OF THE SUBIMAGES 245 9.9.4 WAVELET
COEFFICIENT DOMAIN PROCESSING 246 CONTENTS XIII 9.9.5 HISTOGRAM
THRESHOLDING AND DARK PIXEL REMOVAL 248 9.9.6 PARAMETRIC ART2 CLUSTERING
248 9.9.7 RESULTS 249 9.10 MULTICARRIER COMMUNICATION SYSTEMS 249 9.10.1
OFDM MULTICARRIER COMMUNICATION SYSTEMS 250 9.10.2 WAVELET PACKET-BASED
MCCS 252 9.11 THREE-DIMENSIONAL MEDICAL IMAGE VISUALIZATION 252 9.11.1
THREE-DIMENSIONAL WAVELETS AND ALGORITHMS 255 9.11.2 RENDERING
TECHNIQUES 256 9.11.3 REGION OF INTEREST 258 9.11.4 SUMMARY 258 9.12
COMPUTER PROGRAMS 258 9.12.1 TWO-DIMENSIONAL WAVELET ALGORITHMS 258
9.12.2 WAVELET PACKETS ALGORITHMS 263 REFERENCES 265 10 WAVELETS IN
BOUNDARY VALUE PROBLEMS 267 10.1 INTEGRAL EQUATIONS 268 10.2 METHOD OF
MOMENTS 272 10.3 WAVELET TECHNIQUES 273 10.3.1 USE OF FAST WAVELET
ALGORITHM 273 10.3.2 DIRECT APPLICATION OF WAVELETS 274 10.3.3 WAVELETS
IN SPECTRAL DOMAIN 275 10.3.4 WAVELET PACKETS 280 10.4 WAVELETS ON THE
BOUNDED INTERVAL 280 10.5 SPARSITY AND ERROR CONSIDERATIONS 282 10.6
NUMERICAL EXAMPLES 285 10.7 SEMIORTHOGONAL VERSUS ORTHOGONAL WAVELETS
291 10.8 DIFFERENTIAL EQUATIONS 294 10.9 EXPRESSIONS FOR SPLINES AND
WAVELETS 295 REFERENCES 297 INDEX 301
|
| any_adam_object | 1 |
| author | Goswami, Jaiveda C. Chan, Andrew K. |
| author_facet | Goswami, Jaiveda C. Chan, Andrew K. |
| author_role | aut aut |
| author_sort | Goswami, Jaiveda C. |
| author_variant | j c g jc jcg a k c ak akc |
| building | Verbundindex |
| bvnumber | BV012514822 |
| classification_rvk | SK 450 SK 750 ZN 6010 |
| classification_tum | MAT 428f |
| ctrlnum | (OCoLC)833422185 (DE-599)BVBBV012514822 |
| discipline | Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Book |
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| id | DE-604.BV012514822 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:28:54Z |
| institution | BVB |
| isbn | 0471197483 |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008494923 |
| oclc_num | 833422185 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM DE-M347 DE-573 |
| owner_facet | DE-703 DE-91G DE-BY-TUM DE-M347 DE-573 |
| physical | XVI, 306 S. Ill., graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in microwave and optical engineering A Wiley-Interscience publication |
| spelling | Goswami, Jaiveda C. Verfasser aut Fundamentals of wavelets theory, algorithms, and applications Jaideva C. Goswami ; Andrew K. Chan New York [u.a.] Wiley 1999 XVI, 306 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in microwave and optical engineering A Wiley-Interscience publication Randwertproblem (DE-588)4048395-2 gnd rswk-swf Signalverarbeitung (DE-588)4054947-1 gnd rswk-swf Elektromagnetische Streuung (DE-588)4194512-8 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Bildverarbeitung (DE-588)4006684-8 gnd rswk-swf Digitale Signalverarbeitung (DE-588)4113314-6 gnd rswk-swf Mehrskalenanalyse (DE-588)4416235-2 gnd rswk-swf Filterbank (DE-588)4154389-0 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Zeit-Frequenz-Analyse (DE-588)4626990-3 gnd rswk-swf Signalverarbeitung (DE-588)4054947-1 s Wavelet (DE-588)4215427-3 s DE-604 Algorithmus (DE-588)4001183-5 s Bildverarbeitung (DE-588)4006684-8 s Harmonische Analyse (DE-588)4023453-8 s Zeit-Frequenz-Analyse (DE-588)4626990-3 s Mehrskalenanalyse (DE-588)4416235-2 s Filterbank (DE-588)4154389-0 s Digitale Signalverarbeitung (DE-588)4113314-6 s Randwertproblem (DE-588)4048395-2 s Elektromagnetische Streuung (DE-588)4194512-8 s 1\p DE-604 Chan, Andrew K. Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008494923&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Goswami, Jaiveda C. Chan, Andrew K. Fundamentals of wavelets theory, algorithms, and applications Randwertproblem (DE-588)4048395-2 gnd Signalverarbeitung (DE-588)4054947-1 gnd Elektromagnetische Streuung (DE-588)4194512-8 gnd Wavelet (DE-588)4215427-3 gnd Bildverarbeitung (DE-588)4006684-8 gnd Digitale Signalverarbeitung (DE-588)4113314-6 gnd Mehrskalenanalyse (DE-588)4416235-2 gnd Filterbank (DE-588)4154389-0 gnd Harmonische Analyse (DE-588)4023453-8 gnd Algorithmus (DE-588)4001183-5 gnd Zeit-Frequenz-Analyse (DE-588)4626990-3 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4054947-1 (DE-588)4194512-8 (DE-588)4215427-3 (DE-588)4006684-8 (DE-588)4113314-6 (DE-588)4416235-2 (DE-588)4154389-0 (DE-588)4023453-8 (DE-588)4001183-5 (DE-588)4626990-3 |
| title | Fundamentals of wavelets theory, algorithms, and applications |
| title_auth | Fundamentals of wavelets theory, algorithms, and applications |
| title_exact_search | Fundamentals of wavelets theory, algorithms, and applications |
| title_full | Fundamentals of wavelets theory, algorithms, and applications Jaideva C. Goswami ; Andrew K. Chan |
| title_fullStr | Fundamentals of wavelets theory, algorithms, and applications Jaideva C. Goswami ; Andrew K. Chan |
| title_full_unstemmed | Fundamentals of wavelets theory, algorithms, and applications Jaideva C. Goswami ; Andrew K. Chan |
| title_short | Fundamentals of wavelets |
| title_sort | fundamentals of wavelets theory algorithms and applications |
| title_sub | theory, algorithms, and applications |
| topic | Randwertproblem (DE-588)4048395-2 gnd Signalverarbeitung (DE-588)4054947-1 gnd Elektromagnetische Streuung (DE-588)4194512-8 gnd Wavelet (DE-588)4215427-3 gnd Bildverarbeitung (DE-588)4006684-8 gnd Digitale Signalverarbeitung (DE-588)4113314-6 gnd Mehrskalenanalyse (DE-588)4416235-2 gnd Filterbank (DE-588)4154389-0 gnd Harmonische Analyse (DE-588)4023453-8 gnd Algorithmus (DE-588)4001183-5 gnd Zeit-Frequenz-Analyse (DE-588)4626990-3 gnd |
| topic_facet | Randwertproblem Signalverarbeitung Elektromagnetische Streuung Wavelet Bildverarbeitung Digitale Signalverarbeitung Mehrskalenanalyse Filterbank Harmonische Analyse Algorithmus Zeit-Frequenz-Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008494923&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT goswamijaivedac fundamentalsofwaveletstheoryalgorithmsandapplications AT chanandrewk fundamentalsofwaveletstheoryalgorithmsandapplications |