Applied Walsh analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Heyden
1981
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 265 S. |
| ISBN: | 0855011629 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | CONTENTS
Preface ix
Abbreviations and Symbols xi
Chapter 1. INTRODUCTION 1
1.1. General Remarks 1
1.2. Orthogonal Functions: Historical Remarks 2
1.3. Applications of Walsh Functions 3
1.4. This Work 3
Selected References 4
Chapter 2. WALSH FUNCTIONS 5
2.1. Introduction 5
2.2. Dyadic Representation of Real Numbers 5
2.2.1. Dyadic expansions 6
2.2.2. Dyadic addition 6
2.2.3. Dyadic shift 8
2.3. Walsh Functions 9
2.4. Properties of Walsh Functions 12
2.5. Remarks on Walsh Series 13
2.5.1. Walsh series expansions 13
2.5.2. Parseval s Relation 17
2.5.3. A translation invariant integral 17
2.5.4. Dyadic correlation of periodic signals 18
2.6. On Computing Walsh Coefficients 19
2.7. A Walsh Dirichlet Kernel 22
2.8. Harmonic Ordering of Walsh Functions 24
Selected References 27
V
vi CONTENTS
Chapter 3. WALSH TRANSFORM 29
3.1. Introduction 29
3.2. Generalized Walsh Functions 30
3.3. The Walsh Transform 32
3.3.1. Definition 32
3.3.2. Delta function 32
3.3.3. Properties of Walsh transform 33
3.3.4. Some examples 39
3.4. The Fine Integral 41
3.5. Relations Between Walsh and Fourier Transforms 43
3.6. On Computing Generalized Walsh Transforms 44
3.6.1. Computing from definition 44
3.6.2. Computing via Fourier transform 45
3.7. Discrete Walsh and Hadamard Transforms 46
3.8. Two Dimensional Discrete Walsh Transform 51
3.9. Poisson Sum Formulas for Walsh Analysis 51
Selected References 54
Chapter 4. CERTAIN CONCEPTS IN STOCHASTIC STUDIES 56
4.1. Introduction 56
4.2. Dyadic and Stayadic Correlation 56
4.2.1. General definitions 56
4.2.2. Dyadic and stayadic correlations of ergodic processes 58
4.3. Sequency Spectral Representation 59
4.4. Walsh Characteristic Functions 62
4.5. Sampling Theorems 65
4.5.1. Deterministic case 65
4.5.2. Further discussion 68
4.5.3. Stochastic case 71
4.6. Bounds on Sampling Expansion Truncation Errors 74
4.6.1. Deterministic case 75
4.6.2. Stochastic case 77
4.7. Walsh Sampling Representation for Nonstationary Processes 78
4.7.1. Sampling representation 78
4.7.2. Truncation error bounds 82
Selected References 83
Chapter 5. LINEAR DYADIC INVARIANT SYSTEMS 85
5.1. Introduction 85
5.2. General Analysis 85
5.3. Dyadic and Stayadic Correlation, and Sequency Spectral Analysis 89
5.4. Wide Sense Stationary Processes in LDI Systems 90
5.5. Optimal LDI Systems 91
5.6. The Dyadic Matched Filter 94
5.7. Sequency Filters 96
5.7.1. Generalized ideal sequency filters 96
CONTENTS vii
5.7.2. Walsh Harmuth filters 100
5.7.3. On time sequency relationship 102
5.8. Considerations in Discrete LDI Systems 103
5.8.1. General analysis 104
5.8.2. A state space approach 107
5.9. On Identification of LDI Systems 109
5.10. WDS Processes in Discrete Linear Time Invariant Systems 110
Selected References 112
Chapter 6. WALSH ANALYSIS OF NONLINEAR SYSTEMS 114
6.1. Introduction 114
6.2. A Walsh Characteristic Function Method 114
6.3. A Matrix Method 118
6.4. Quasi Linear Approximation 123
6.5. Walsh Analysis of Power Law Systems 127
6.5.1. General analysis 127
6.5.2. A truncated Walsh series expansion 130
6.6. A Quantizer Analysis 132
6.6.1. Walsh transform of nonlinearity 133
6.6.2. Stayadic correlation analysis 133
6.6.3. On a certain useful integral 134
6.7. Identification of Nonlinear Systems 136
6.7.1. General analysis 136
6.7.2. Determination oftheVoltera kernels 139
6.8. Epilogue 144
Selected References 146
Chapter 7. APPLICATIONS OF WALSH FUNCTIONS TO
STATISTICAL PROB LEMS 148
7.1. Introduction 148
7.2. Statistical Properties of Rademacher Functions 148
7.3. Statistical Properties of Walsh Functions 151
7.4. Probability Transformations 152
7.5. Walsh Series Expansions of Probability Distributions 154
7.5.1. Walsh expansion of a univariate PDF 156
7.5.2. Walsh expansion of a bivariate PDF 161
7.6. Applications to Nonlinear Transformations (Systems) 166
7.6.1. Some generalities 166
7.6.2. General moments of nonlinear systems 168
Selected References 172
Chapter 8. HAAR FUNCTIONS 174
8.1. Introduction 174
8.2. Haar Functions 174
8.3. Haar Series Expansion 177
viii CONTENTS
8.4. Relations Between Haar and Walsh Functions 180
8.5. Discrete Haar Transform 181
8.6. On an Alternative Definition of Haar Functions 183
8.7. On Applications of Haar Functions 184
Selected References 185
Chapter 9. RELATION BETWEEN WALSH AND FOURIER SPECTRA 187
9.1. Introduction 187
9.2. Trigonometric Fourier Series 187
9.3. Interrelationships of Walsh and Fourier Series 189
9.4. Relations Between Discrete Walsh and Fourier Transforms 194
9.5. Comparison of Various Forms of Walsh and Fourier Transforms 196
9.6. Relations Between the DWT and the z Transform 200
Selected References 205
Chapter 10. SOME APPLICATIONS IN COMMUNICATIONS 207
10.1. Introduction 207
10.2. Multiplexing 208
10.2.1. Time division multiplexing 208
10.2.2. Frequency division multiplexing 210
10.2.3. Sequency division multiplexing 211
10.2.4. Some general remarks on multiplexing 214
10.3. Binary and Data Coding 215
10.3.1. Preliminary notions in coding theory 215
10.3.2. Binary and Walsh codes 216
10.3.3. Data coding 218
10.4. Image Transmission 219
10.4.1. Representation of continuous images 219
10.4.2. Certain digital image processing aspects 220
10.5. Signal Processing 226
10.5.1. ECG analysis 227
10.5.2. Speech processing 230
10.6. Epilogue 233
Selected References 235
Appendix A. Fast Hadamard Transform: An Algorithm 239
Appendix B. Kramer s Generalized Sampling Theorem 242
Appendix C Discrete Fourier Transform and Properties 244
Appendix D. Karhunen Loeve Transform (Expansion) 248
Supplementary Selected References 251
Subject Index 259
Author Index 263
|
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| id | DE-604.BV002266470 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:43:03Z |
| institution | BVB |
| isbn | 0855011629 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001489348 |
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| physical | XIV, 265 S. |
| publishDate | 1981 |
| publishDateSearch | 1981 |
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| publisher | Heyden |
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| spelling | Maqusi, Mohammad Verfasser aut Applied Walsh analysis London Heyden 1981 XIV, 265 S. txt rdacontent n rdamedia nc rdacarrier Walsh functions Walsh-Transformation (DE-588)4627153-3 gnd rswk-swf Walsh-Transformation (DE-588)4627153-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001489348&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Maqusi, Mohammad Applied Walsh analysis Walsh functions Walsh-Transformation (DE-588)4627153-3 gnd |
| subject_GND | (DE-588)4627153-3 |
| title | Applied Walsh analysis |
| title_auth | Applied Walsh analysis |
| title_exact_search | Applied Walsh analysis |
| title_full | Applied Walsh analysis |
| title_fullStr | Applied Walsh analysis |
| title_full_unstemmed | Applied Walsh analysis |
| title_short | Applied Walsh analysis |
| title_sort | applied walsh analysis |
| topic | Walsh functions Walsh-Transformation (DE-588)4627153-3 gnd |
| topic_facet | Walsh functions Walsh-Transformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001489348&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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