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Aqaian S., Astola J., Egiazarian K. — Binary polynomial transforms and nonlinear digital filters
Aqaian S., Astola J., Egiazarian K. — Binary polynomial transforms and nonlinear digital filters



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Название: Binary polynomial transforms and nonlinear digital filters

Авторы: Aqaian S., Astola J., Egiazarian K.

Язык: en

Рубрика: Математика/Численные методы/Вейвлеты, обработка сигналов/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 329

Добавлена в каталог: 26.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\rho$-auto-correlation      68 71 74 77
$\rho$-auto-correlation, column-vector      69
$\rho$-cross-correlation      68 71 74
$\rho$-cross-correlation, column-vectors      70
$\tau$-polynomial logical functions      12
$\tau$-polynomial logical matrix      15
$\tau$-polynomial logical matrix, complementary      10
$\vee$-auto-correlation      70
$\wedge$-cross-correlation      70
(a,b,$\tau$)-polynomial functions, arithmetical      9
(a,b,$\tau$)-polynomial functions, logical      9
(a,b,$\tau$)-polynomial matrix      9
(a,b,$\tau$)-polynomial matrix, complementary      9
(s,n,$\tau$,$\sigma$)-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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