Binary polynomial transforms and nonlinear digital filters:
This unique reference offers a unified presentation of the theory of binary polynomial transforms and details their numerous applications in nonlinear signal processing. Binary Polynomial Transforms and Nonlinear Digital Filters introduces the Rademacher logical functions...considers fast algorithms...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Dekker
1995
|
| Schriftenreihe: | Pure and applied mathematics
191 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | This unique reference offers a unified presentation of the theory of binary polynomial transforms and details their numerous applications in nonlinear signal processing. Binary Polynomial Transforms and Nonlinear Digital Filters introduces the Rademacher logical functions...considers fast algorithms for computing Rademacher and polynomial logical functions...focuses attention on general auto- and cross-correlation functions...analyzes Boolean functions via binary polynomial transforms...studies standard median and order statistic filters...explores the statistical properties of stack filters...and much more. |
| Beschreibung: | XIX, 302 S. |
| ISBN: | 082479642X |
Internformat
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| 490 | 1 | |a Pure and applied mathematics |v 191 | |
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Datensatz im Suchindex
| _version_ | 1804124738261352448 |
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| adam_text | BINARY POLYNOMIAL TRANSFORMS AND NONLINEAR DIGITAL FILTERS S. AGAIAN
TUFTS UNIVERSITY MEDFORD, MASSACHUSETTS, AND THE ARMENIAN ACADEMY OF
SCIENCES YEREVAN, ARMENIA J. ASTOLA TAMPERE UNIVERSITY OF TECHNOLOGY
TAMPERE, FINLAND K. EGIAZARIAN TAMPERE UNIVERSITY OF TECHNOLOGY TAMPERE,
FINLAND, AND THE ARMENIAN ACADEMY OF SCIENCES YEREVAN, ARMENIA MARCEL
DEKKER, INC. NEW YORK* BASEL * HONG KONG CONTENTS PREFACE V LIST OF
SYMBOLS AND ABBREVIATIONS XIII INTRODUCTION XVII I BINARY POLYNOMIAL
TRANSFORMS 1 1 BINARY POLYNOMIAL ARITHMETICAL AND LOGICAL FUNCTIONS AND
MATRICES 3 1.1 INTRODUCTION 3 1.2 RADEMACHER FUNCTIONS AND MATRICES 4
1.3 ARITHMETICAL AND LOGICAL BINARY POLYNOMIAL FUNCTIONS. CON-
STRUCTIONS USING ONE BINARY OPERATION 9 1.3.1 WALSH FUNCTIONS AND
MATRICES 10 1.3.2 POLYNOMIAL LOGICAL FUNCTIONS AND MATRICES 11 1.4
BINARY POLYNOMIAL LOGICAL FUNCTIONS AND MATRICES. CON- STRUCTIONS USING
TWO OPERATIONS 16 1.5 BINARY POLYNOMIAL LOGICAL FUNCTIONS AND MATRICES.
EXTEN- SIONS OF DIMENSION 24 1.5.1 INTERVAL SPLICING MATRICES 24 1.5.2
INTERVAL ABSORBING MATRICES 27 2 FAST ALGORITHMS AND COMPLEXITY OF
BINARY POLYNOMIAL TRANS- FORMS 35 2.1 INTRODUCTION 35 2.2 GENERAL
APPROACH TO THE FAST ALGORITHMS OF BINARY POLYNO- MIAL TRANSFORMS 36 2.3
FAST RADEMACHER TRANSFORMS 38 2.4 FAST WALSH TRANSFORMS 39 2.5 FAST
CONJUNCTIVE TRANSFORMS 43 2.6 FAST INTERVAL TRANSFORMS 46 2.7 FAST
DISJUNCTIVE-CONJUNCTIVE TRANSFORMS 51 2.8 LOWER BOUNDS OF THE COMPLEXITY
OF SOME BINARY POLYNOMIAL TRANSFORMS 58 VIII CONTENTS 3 LOGICAL
CORRELATIONS AND BINARY POLYNOMIAL TRANSFORMS 63 3.1 INTRODUCTION 63 3.2
ARITHMETICAL AND LOGICAL CORRELATION FUNCTIONS 64 3.2.1 ARITHMETICAL
AUTO- AND CROSS-CORRELATION FUNCTIONS . 64 3.2.2 LOGICAL AUTO- AND
CROSS-CORRELATION FUNCTIONS . . . . 64 3.2.3 RELATIONS BETWEEN THE
ARITHMETICAL AND LOGICAL AUTO- CORRELATION FUNCTIONS 65 3.3 GENERAL
AUTO- AND CROSS-CORRELATION FUNCTIONS 67 3.3.1 DEFINITIONS 67 3.3.2
PROPERTIES OF LOGICAL /^CORRELATION 71 3.4 TRANSFORM METHOD FOR
COMPUTATION OF CROSS-CORRELATION . 71 3.4.1 COMPUTATION OF GENERAL
CROSS-CORRELATION 71 3.4.2 COMPUTATION OF LOGICAL CROSS-CORRELATION
BASED ON ANY BOOLEAN OPERATION 74 3.5 POWER-SPECTRUM AND GENERAL
WIENER-KHINCHINE THEOREM . 75 3.6 COMMENTS 78 II BINARY POLYNOMIAL
TRANSFORMS AND DIGITAL LOGIC 85 4 SPECTRAL METHODS IN ANALYSIS OF
BOOLEAN FUNCTIONS 87 4.1 INTRODUCTION 87 4.2 LINEAR BOOLEAN FUNCTIONS 97
4.3 POSITIVE (MONOTONE) BOOLEAN FUNCTIONS 99 4.4 SELFDUAL BOOLEAN
FUNCTIONS 100 4.5 SYMMETRIC BOOLEAN FUNCTIONS 101 4.6 ANALYSIS OF
FICTITIOUS VARIABLES 103 4.7 PARTIAL DERIVATIVES OF BOOLEAN FUNCTIONS .I
106 4.8 ACTIVITIES OF THE VARIABLES OF BOOLEAN FUNCTIONS 109 4.8.1 CHOW
PARAMETERS AND WEIGHTED CHOW PARAMETERS OF A BOOLEAN FUNCTION ILL 4.9
TRANSFER FROM ONE NORMAL FORM TO ANOTHER AND THE LOGICAL OPERATIONS OVER
THE NORMAL FORMS 112 4.9.1 CONNECTIONS BETWEEN NORMAL FORMS OF BOOLEAN
FUNC- TIONS 113 4.9.2 LOGICAL OPERATIONS OVER NORMAL FORMS 115 5
SPECTRAL METHODS IN MINIMIZATION OF BOOLEAN FUNCTIONS 117 5.1
INTRODUCTION 117 5.2 GENERAL SPECTRAL ALGORITHMS FOR CONSTRUCTION OF THE
ABBRE- VIATED DISJUNCTIVE AND CONJUNCTIVE NORMAL FORMS OF BOOLEAN
FUNCTION 121 CONTENTS IX 5.3 DEADLOCK TESTS AND ABBREVIATED NORMAL FORMS
OF BOOLEAN FUNCTIONS 130 5.3.1 UNCONDITIONAL DEADLOCK TESTS FOR TABLES
130 5.3.2 ABBREVIATED DISJ UNCTIVE AND CONJ UNCTIVE NORMAL FORMS OF
BOOLEAN FUNCTIONS WITH A SMALL NUMBER OF ONES (ZE- ROS) 136 5.4 DEADLOCK
AND MINIMAL DISJUNCTIVE AND CONJUNCTIVE NORMAL FORMS OF BOOLEAN
FUNCTIONS 142 5.5 MINIMIZATION OF POSITIVE (MONOTONE) BOOLEAN FUNCTIONS
. . 147 5.5.1 MINIMAL DISJUNCTIVE AND CONJUNCTIVE NORMAL FORMS OF
POSITIVE BOOLEAN FUNCTIONS 147 5.5.2 MINIMIZATION OF THE DUAL OF A
POSITIVE BOOLEAN FUNCTION 150 5.6 QUASI-MINIMIZATION OF BOOLEAN
FUNCTIONS 152 5.7 REED-MULLER POLYNOMIALS OF BOOLEAN FUNCTIONS 161 5.7.1
SPECTRAL APPROACH TO THE CONSTRUCTION OF REED-MULLER POLYNOMIALS 161
5.7.2 SPECTRAL APPROACH TO GENERALIZED REED-MULLER POLY- NOMIALS
CONSTRUCTION 163 5.8 COMMENTS 167 III APPLICATIONS IN NONLINEAR DIGITAL
FILTERING 171 6 MEDIAN AND ORDER STATISTIC FILTERS 173 6.1 INTRODUCTION
173 6.2 STANDARD MEDIAN AND ORDER STATISTIC FILTERS 175 6.2.1 STANDARD
MEDIAN NITERS IN REAL DOMAIN 175 6.2.2 STANDARD MEDIAN FILTERS IN BINARY
DOMAIN ; 176 6.2.3 STANDARD MEDIAN FILTERS IN COMPLEX DOMAIN 178 6.2.4
ORDER STATISTIC FILTERS 179 6.2.5 TWO-DIMENSIONAL MEDIAN AND ORDER
STATISTIC FILTERS . 179 6.3 HISTOGRAM-TYPE ALGORITHMS OF FAST MEDIAN AND
ORDER STATIS- TIC FILTERING 182 6.3.1 RADIX ALGORITHMS FOR FINDING
MEDIAN AND ORDER STATISTICS 182 6.3.2 HISTOGRAM-TYPE ALGORITHMS FOR
ONE-DIMENSIONAL RUN- NING MEDIAN AND ORDER STATISTIC FILTERING 192 6.3.3
HISTOGRAM- TYPE ALGORITHMS FOR TWO-DIMENSIONAL RUN- NING MEDIAN AND
ORDER STATISTIC FILTERING 196 6.4 DECOMPOSITION ALGORITHMS OF MEDIAN AND
ORDER STATISTIC FILTERING 198 6.4.1 DECOMPOSITION ALGORITHMS FOR FINDING
MEDIAN AND OR- DER STATISTIC 198 CONTENTS 6.4.2 DECOMPOSITIONAL
ALGORITHMS FOR RUNNING MEDIAN AND ORDER STATISTIC FILTERING 202 7
WEIGHTED ORDER STATISTIC AND STACK FILTERS 209 7.1 WEIGHTED MEDIAN AND
WEIGHTED ORDER STATISTIC FILTERS . . 209 7.1.1 WEIGHTED MEDIAN FILTERS
IN THE REAL DOMAIN 209 7.1.2 WEIGHTED MEDIAN FILTERS IN BINARY DOMAIN
210 7.1.3 WEIGHTED MEDIAN FILTERS IN COMPLEX DOMAIN . . . . 211 7.1.4
WEIGHTED ORDER STATISTIC FILTERS 212 7.2 HISTOGRAM-TYPE ALGORITHMS FOR
FINDING WEIGHTED ORDER STATIS- TICS 213 7.3 HISTOGRAM-TYPE ALGORITHMS
FOR RUNNING WEIGHTED ORDER STATISTIC FILTERING 214 7.3.1 RUNNING
ALGORITHM FOR LINEARLY DISTRIBUTED WEIGHTS . 215 7.3.2 RUNNING ALGORITHM
FOR EXPONENTIALLY DISTRIBUTED WEIGHTS 217 7.3.3 RUNNING ALGORITHM FOR
COMBINATION OF WEIGHTS . . . 218 7.3.4 HISTOGRAM-TYPE ALGORITHMS FOR
TWO-DIMENSIONAL RUN- NING WEIGHTED ORDER STATISTIC FILTERING 221 7.4
DECOMPOSITION ALGORITHMS OF WEIGHTED ORDER STATISTIC FIL- TERING 226 7.5
STACK FILTERS 229 7.5.1 STACK FILTERS AND THRESHOLD DECOMPOSITION 229
7.6 DECOMPOSITION METHODS FOR STACK FILTERING 231 7.6.1 DECOMPOSITION
METHODS OF STACK FILTERING FOR FIXED WINDOW 231 7.6.2 DECOMPOSITION
METHODS OF STACK FILTERING FOR RUNNING WINDOW 237 7.7 SPECTRAL APPROACH
TO STACK AND WEIGHTED ORDER STATISTIC FILTERS 240 8 STATISTICAL
PROPERTIES OF STACK FILTERS 247 8.1 INTRODUCTION 247 8.2 NOISE
ATTENUATION FOR ORDER STATISTICS 248 8.3 MAXIMUM LIKELIHOOD ESTIMATORS
250 8.4 OUTPUT DISTRIBUTION FUNCTIONS OF WEIGHTED ORDER STATISTIC AND
STACK FILTERS : 253 8.4.1 OUTPUT DISTRIBUTION FUNCTIONS OF A STACK
FILTER . . . . 253 8.4.2 OUTPUT DISTRIBUTION FUNCTION OF A WEIGHTED
ORDER STATIS- TIC FILTER 254 8.5 JOINT DISTRIBUTIONS OF STACK FILTERS
257 8.5.1 DEFINITIONS AND NOTATIONS 257 8.5.2 JOINT CUMULATIVE
DISTRIBUTION OF L STACK FILTERS . . . . 258 CONTENTS XI 8.6 SPECTRAL
APPROACH TO THE CALCULATION OF THE JOINT DISTRIBU- TION OF STACK FILTERS
262 8.7 SELECTION PROBABILITIES OF STACK FILTERS 266 8.7.1 DEFINITIONS
AND PROPERTIES 266 8.7.2 SELECTION PROBABILITIES OF WEIGHTED ORDER
STATISTIC FILTERS 267 8.7.3 PARTIAL DERIVATIVES OF PBF AND SELECTION
PROBABILITY SETS OF STACK FILTERS 273 8.7.4 ACTIVITIES OF VARIABLES OF
BOOLEAN FUNCTIONS AND THE COMBINATION MATRIX OF CONTINUOUS STACK FILTERS
. . . . 277 8.7.5 WEIGHTED ACTIVITIES OF VARIABLES AND JOINT SELECTION
PROBABILITY MATRIX OF STACK FILTERS 278 8.7.6 SAMPLE SELECTION
PROBABILITY VECTORS AND WEIGHTED CHOW PARAMETERS 279 8.8 SPECTRAL
APPROACH TO THE CALCULATION OF SELECTION PROBABILITIES 281 8.8.1
CONSTRUCTION OF SELECTION PROBABILITY SETS FOR CONTIN- UOUS STACK
FILTERS 281 8.8.2 CONSTRUCTION OF JOINT SELECTION PROBABILITY MATRIX FOR
CONTINUOUS STACK AND WOS FILTERS 282 8.8.3 CONSTRUCTION OF SAMPLE
SELECTION PROBABILITY VECTOR FOR CONTINUOUS STACK FILTERS 286 8.8.4
CONSTRUCTION OF RANK SELECTION PROBABILITY VECTOR FOR CONTINUOUS STACK
FILTERS 287 8.9 COMMENTS 288 INDEX 297
|
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| author | Agaian, S. Astola, Jaakko Egiazarian, Karen |
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| discipline | Informatik Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
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| id | DE-604.BV010318684 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:50:26Z |
| institution | BVB |
| isbn | 082479642X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006866461 |
| oclc_num | 32086644 |
| open_access_boolean | |
| owner | DE-384 DE-12 DE-11 |
| owner_facet | DE-384 DE-12 DE-11 |
| physical | XIX, 302 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Agaian, S. Verfasser aut Binary polynomial transforms and nonlinear digital filters S. Agaian ; J. Astola ; K. Egiazarian New York u.a. Dekker 1995 XIX, 302 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 191 This unique reference offers a unified presentation of the theory of binary polynomial transforms and details their numerous applications in nonlinear signal processing. Binary Polynomial Transforms and Nonlinear Digital Filters introduces the Rademacher logical functions...considers fast algorithms for computing Rademacher and polynomial logical functions...focuses attention on general auto- and cross-correlation functions...analyzes Boolean functions via binary polynomial transforms...studies standard median and order statistic filters...explores the statistical properties of stack filters...and much more. Transformations (mathématiques) ram Digital filters (Mathematics) Nonlinear theories Signal processing Digital techniques Transformations (Mathematics) Nichtlineares Digitalfilter (DE-588)4260108-3 gnd rswk-swf Binäre Transformation (DE-588)4390389-7 gnd rswk-swf Nichtlineares Digitalfilter (DE-588)4260108-3 s Binäre Transformation (DE-588)4390389-7 s DE-604 Astola, Jaakko Verfasser aut Egiazarian, Karen Verfasser aut Pure and applied mathematics 191 (DE-604)BV000001885 191 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006866461&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Agaian, S. Astola, Jaakko Egiazarian, Karen Binary polynomial transforms and nonlinear digital filters Pure and applied mathematics Transformations (mathématiques) ram Digital filters (Mathematics) Nonlinear theories Signal processing Digital techniques Transformations (Mathematics) Nichtlineares Digitalfilter (DE-588)4260108-3 gnd Binäre Transformation (DE-588)4390389-7 gnd |
| subject_GND | (DE-588)4260108-3 (DE-588)4390389-7 |
| title | Binary polynomial transforms and nonlinear digital filters |
| title_auth | Binary polynomial transforms and nonlinear digital filters |
| title_exact_search | Binary polynomial transforms and nonlinear digital filters |
| title_full | Binary polynomial transforms and nonlinear digital filters S. Agaian ; J. Astola ; K. Egiazarian |
| title_fullStr | Binary polynomial transforms and nonlinear digital filters S. Agaian ; J. Astola ; K. Egiazarian |
| title_full_unstemmed | Binary polynomial transforms and nonlinear digital filters S. Agaian ; J. Astola ; K. Egiazarian |
| title_short | Binary polynomial transforms and nonlinear digital filters |
| title_sort | binary polynomial transforms and nonlinear digital filters |
| topic | Transformations (mathématiques) ram Digital filters (Mathematics) Nonlinear theories Signal processing Digital techniques Transformations (Mathematics) Nichtlineares Digitalfilter (DE-588)4260108-3 gnd Binäre Transformation (DE-588)4390389-7 gnd |
| topic_facet | Transformations (mathématiques) Digital filters (Mathematics) Nonlinear theories Signal processing Digital techniques Transformations (Mathematics) Nichtlineares Digitalfilter Binäre Transformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006866461&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
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