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| Авторизация |
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| Aqaian S., Astola J., Egiazarian K. — Binary polynomial transforms and nonlinear digital filters |
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| Предметный указатель |
 -auto-correlation 68 71 74 77
-auto-correlation, column-vector 69
-cross-correlation 68 71 74
-cross-correlation, column-vectors 70
 -polynomial logical functions 12
-polynomial logical matrix 15
-polynomial logical matrix, complementary 10
 -auto-correlation 70
 -cross-correlation 70
(a,b,)-polynomial functions, arithmetical 9
(a,b,)-polynomial functions, logical 9
(a,b,)-polynomial matrix 9
(a,b,)-polynomial matrix, complementary 9
(s,n,, )-polynomiallogical functions 16
Absorption 91
Activity of variables of Boolean function 109—112
Activity, weighted 110—113 279
Antivalent normal form (ANF) 95 112
Appending strategy 175 180
Associativity 91
Asymptotically optimal algorithm 59
Auto-correlation 63
Auto-correlation, arithmetical 65 66
Auto-correlation, dyadic 63
Auto-correlation, logical 65 66
Besslich's algorithm 152
Binary cube (n-cube) 27 28 87 122
Binary polynomial transform 97
Binary polynomial transform, fast algorithms 36 37
Binary vector code 87
Binomial matrix 271
Blake — Poresko's method 96
Boolean cube see Binary cube
Characteristic vector 136
Chen's algorithm 205 240
Chow parameters 92 111
Chow parameters, weighted 112 279
Classification of Boolean functions 167
Commutativity 91
Conjunction 95
Conjunctive matrix 13 15 22 43 75 134 154
Conjunctive normal form (CNF) 94 96 112 119 231
Conjunctive normal form, abbreviated (contracted) 121 127 132 136 142
Conjunctive normal form, deadlock (irredundant) 121 144—145
Conjunctive normal form, minimal 119 149
Conjunctive normal form, shortest 119
Conjunctive transform 45—47 60 61 148 242 265 283
Conjunctive transform, complexity 60—61
Conjunctive transform, fast algorithm 44—46
Conjunctive transform, graph of fast algorithm 46
Conjunctive transform, two-dimensional 158 162
Convolution linear 268 271 285
Cooley, Tukey 35
Correlation 63
Correlation, auto- 63
Correlation, cross- 63
Correlation, logical 63
Covering 27 119 152
Cross-correlation, arithmetical 64
Cross-correlation, dyadic 65
Cross-correlation, logical 65
De Morgan rule 18
Decomposition algorithms (methods) 174 198 202 203 226 231 237
Density function of median 249
Density function, joint 250
Detail preservation 248
Discrete orthogonal transform 167
Disjunction 95
Disjunctive matrix 22
Disjunctive normal form (DNF) 26 94 95 112 119 231
Disjunctive normal form, abbreviated (contracted) 27 28 121 122 127 136 138 141
Disjunctive normal form, deadlock (irredundant) 121 142 144—145
Disjunctive normal form, minimal 119 142 146—147 242 253
Disjunctive normal form, shortest 119 146
Disjunctive transform 61
Disjunctive-conjunctive transforms 51
Disjunctive-conjunctive transforms, complexity 58
Disjunctive-conjunctive transforms, fast algorithms 53—54
Distribution function, asymptotic 247
Distribution function, common 251
Distribution function, joint cumulative 258—262
Distribution function, output 253—256
Distributivity 91
Dual boolean function 93
Dual boolean function, positive 150
Edge preservation 174
Elementary symmetric boolean function 101
Elementary symmetric boolean matrix 102 256
Elementary symmetric boolean transform 102
Elementary symmetric boolean transform, two-dimensional 102
Energy spectrum 77
Equivalent normal form (ENF) 96 112
Essential variable 95
Expectation 249
Expected value 64—65 68 75
Fast algorithm 35
Fast Fourier transform (FFT) 35 77
Fibonacci, p-codes 190 198 205—208 228—229 234 240
Fibonacci, p-numbers 187 205—208 240
Fictitious variable 95 103—104 106
Filters, digital 167
Filters, linear 167 247
Filters, nonlinear 174
Fourier, basis 35
Fourier, power spectrum 63
Gaussian input 248
Generating functions 255—256 268 285
Good's theorem 35—37 40 44
Gray code 30 90
Hadamard matrix 10
Hadamard ordering 31
Hamming weight 101 110 254
Histogram (h-array) 182 213 225
Histogram algorithm 193 221
Histogram binary tree (b-array) 183
Histogram, modified (weighted) 213
Huang's algorithm 225
Identity matrix 15 29
Identity matrix, opposite diagonal 15
Implicant 95
Implicant prime 95 120 146 152 155
Implicant prime, quasi-essential 152 156
Implicant table 146
Implicent 97 120
Impulsive noise 174
Independent and identically distributed (i.i.d.) 261
interval 122
Interval functions, absorbing 27
Interval functions, splicing 26
Interval matrices, absorbing 24 27—28 49—50 121
Interval matrices, absorbing splicing 26 27 46 121
Interval splicing 48—49
| Interval splicing, fast algorithm 48—49
Interval splicing, graph of fast algorithm 49
Interval transforms, absorbing 50
Interval transforms, fast algorithm 50
Interval transforms, graph of fast algorithm 51
Interval, maximal 27
Interval, maximal conjunctive 120
Interval, minimal disjunctive 120
Karnaugh map 89—90
Kronecker, delta function 125 134 154
Kronecker, power of matrix 9 29
Kronecker, product of matrices 9 28 35 37 52
Laplacian noise 174 252
Linear boolean function 92 97—99
Linear computation 59
Linear form 58
Linear transform 59 66
Linearly separable boolean function (LSBF) 92 211
Logical operations 115
majority 178
Maximum likelihood estimate 174 250
Maxterm 95 120
Median Filter 174—205 247
Median filter, standard 209
Median filter, weighted 209—214
Median, standard 175
Median, weighted 209 272
Minimal conjunctive normal form 119
Minimal disjunctive normal form 119
Minimization of boolean function 117
Minterm 95 120
Minterm, uncovered 161
Negation 91
Noise 247
Noise attenuation 248
Normal form 96 112 115 117
Normal form, abbreviated (contracted) 96 117
Normal form, complexity 96
Normal form, deadlock (irredundant) 97 119
Normal form, minimal 97 117
Normal form, perfect 96
Normal form, shortest 97 117
Order statistic filter 179—210
Order statistics 179
Orderings 30—31
Paley 63
Paley ordering 10 31
Partial derivative of boolean function 106—110 273 281
Partial derivative of boolean function, matrix 107
Partial derivative of boolean function, transform 108
Partial derivative of boolean function, vector 108
Pascal triangle 14
Positive boolean function 92—95 99—100 147 149 231 234 240 253 263 273 287
Positive boolean function, isobaric 238
Post's classes 97
Power spectrum 63 77
Precedence relation 26
Prethrcsholding operator 273
Quasi-minimization of boolean function 152 156 161
Quine — McClusky method 146
Rademacher functions, (a,b)- 5
Rademacher functions, classical 5
Rademacher matrices, (0,1)- 256 287
Rademacher matrices, (a,b)- 7
Rademacher matrices, classical 8
Rademacher transform 38
Rademacher transform, fast algorithm 39
Rademacher transform, graph of fast algorithm 39
Radix (histogram-type) methods 174 182
Rao-Rao array (m-array) 184 195 213
Rao-Rao array, modified (weighted) 214
Reed — Muller polynomial 95 161 163
Reed — Muller polynomial, generalized 164—167
Reed — Muller transform see conjunctive transform
Root signals 174
Selection probabilities 248
Selection probabilities, joint 248 278 282
Selection probabilities, matrix 248 277 283
Selection probabilities, rank 248 266 287
Selection probabilities, sample 248 266 279 287
Selection probabilities, sets 266
Selfdual boolean function 92—93 100—101
Shift operator 71
Sparse matrix 35
Stack filters 229—242
Stack filters, continuous 257 266 277
Stacking property 231
Stationary random process 64
Symmetric Boolean function 92—93 101 103
Symmetric boolean function, elementary 101
System of representatives 131
System of representatives, deadlock 131
Ternary representation 24
Ternary vector 89
Tests 130
Tests, deadlock 130 134—137 141 145
Tests, minimal 131
Threshold decomposition 176 198 229 233 234 253
Threshold decomposition, binary-tree 227 233
Threshold operator 12 264
Tolerance intervals of boolean function 119
Transform discrete 35
Truth table 27 28 115 283 287
Tukey 247
Variables (literals) 95
Variance 249
Vector of structure 244
Veich diagram 90
Walsh functions 10 92
Walsh matrix 11 134
Walsh ordering 10 31
Walsh power spectrum 77
Walsh transform (spectrum) 105 136 153 167
Walsh transform, two-dimensional 104 156
Walsh — Hadamard transform 40 75
Walsh — Hadamard transform, complexity 61
Walsh — Hadamard transform, fast algorithm 41—43
Walsh — Hadamard transform, fast algorithm graph 43
Weak superposition property 231
Weighted median (WM) 209 225 272
Weighted median filter 210—218
Weighted order statistics (WOS) 212
Weighted order statistics, filter 213 221 226 229
Wiener 63
Wiener — Khinchine theorem 63 77
Zhegalkin polynomial see Reed — Muller polynomial
{s,n)-disjunctive-conjunctive complementary functions 18
{s,n)-disjunctive-conjunctive complementary matrix 18
{s,n)-disjunctive-conjunctive discrete functions 19
{s,n)-disjunctive-conjunctive functions 18
{s,n)-disjunctive-conjunctive matrix 18
“Don't care” vectors 87
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