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| Gray R.M., Davisson L.D. — Introduction to statistical signal processing |
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| Предметный указатель |
 response 102
 function 64
a.m.s. 431
Abstract space 389
Additive, finite 42
Additivity 18 42
Additivity, countable 43
Additivity, finite 18
Affine 226
Algebra 24
Alphabet 104
Alphabet, continuous 116
Alphabet, discrete 116
Alphabet, mixed 116
Amplitude, continuous 116
Amplitude, discrete 116
Area 11
ARMA random process 348
Asymptotically mean stationary 431
Asymptotically uncorrelated 256 258
Autocorrelation matrix 227
Autoregressive 160 295
Autoregressive filter 346
Autoregressive random process 348
Average, probabilistic 47
Average, statistical 47
Axioms 18
Axioms of probability 25
Balakrishnan A.V. 305
Bayes risk 136
Bayes' rule 131 133 136
Bernoulli process 94 158
binomial 427
Binomial coefficient 427
Binomial counting process 162 349
Bit 184
Bonferoni inequality 78
Borel field 37
Borel sets 37
Borel space 56
Borel — Cantelli lemma 247
Borel — Cantelli lemma, categorical 390
Cauchy — Schwarz inequality 206
Causal 410
CDF 81 107 119
Central limit theorem 199 235
Chain rule 131 162
Channel, noisy 135
Characteristic function 148 150 197
Chernoff inequality 249
Chi-squared 113
Collectively exhaustive 401
Complement 394
Complementation 394
complete 77
Complete the square 126 140 152
Completion 77
Conditional differential entropy 270
Conditional expectation 210
Conditional mean 142
Conditional pmf 130
Conditional probability 71
Conditional probability, nonelementary 168 169
Conditional variance 142
Consistency 16 121
Continuity 43
Continuity from above 45
Continuity from below 45
Continuous time 116
Convergence in distribution 236
Convergence in mean square 240
Convergence in probability 240
Convergence, almost everywhere 240
Convergence, almost surely 240
Convergence, pointwise 240
Convergence, w.p. 1 240
Convergence, with probability one 240
Convolution 406
Convolution, discrete 138
Convolution, modulo 2 138
Convolution, sum 138
Coordinate function 100
Correlation 203
Correlation coefficient 133
Countable 400
Counting process 163
Covariance 205
Cross-correlation 317
Cross-covariance 214
Cross-spectral density 317
Cumalitive distribitution function 119
Cumulative distribution function 81 107
Decision rule 135
Decreasing sets 33
DeMorgan's law 399
Density, mass 11
Dependent 92
Derived distribution 21 88
Detection 135
Difference, symmetric 396
Differential entropy 209
Dirac delta 66
Directly given 22
Discrete spaces 28
Discrete time 116
Disjoint 394 401
Distance 78
distribution 87 105 117
Distribution, convergence in 236
Distribution, joint 122
Distribution, marginal 122
Domain 401
Domain of definition 21
Dominated convergence theorom 202
Dot product 403
Doubly exponential 428
Doubly stochastic 375
Eigenvalue 404
Eigenvector 404
Element 389
Elementary events 23
Elementary outcomes 23
Empty set 393
eq:2ndorder 252
Equivalent random variables 89
Ergodic decomposition 376
Ergodic theorem 190
Ergodic theorems 187
Ergodicity 373
Error, mean squared 216
Estimate, minimum mean squared error 219
Estimation 146
Estimation, maximum a posteriori 147
Event 23
Event space 12 23 31
Event space, trivial 27
Events, elementary 23
Expectation 46 56 187 189
Expectation, conditional 210
Expectation, fundamental theorem of 195
Expectation, iterated 211
Expectation, nested 211
Expected value 190
Experiment 12 26
Exponential 428
Field 24
Filter, autoregressive 346
Filter, linear 406
Filter, moving average 344
Filter, transversal 345
| FIR 344
Fourier transform 148 151 308
Function 401
Function, identity 47
Function, measurable 98
Fundamental theorem of expectation 195
Gamma 428
Gaussian 158 428
Gaussian random vectors 152
Gaussian, jointly 213
Geometric 427
Hamming weight 55 160
Hard limiter 99
Hidden Markov model 167
Identically distributed 89
Identity function 47
Identity mapping 88
IID 94 128 158
IIR 344
Image 402
Impulse response 406
Increasing sets 32
Increments 351
Independence 70 127
Independence, linear 204
Independent 127 351
Independent and stationary increments 350
Independent identically distributed 94 128
Independent increments 351
Independent random variables 127
Independent, stationary 351
Indicator function 46 196
Induction 50
Inequality, Tchebychev 242
Infinite, countably 400
Inner product 403
Integral, Lebesgue 58 423
Intersection 394
interval 393
Interval, closed xv 393
Interval, half-closed 393
Interval, half-open 393
Interval, open xv 393
Inverse image 87 402
Inverse image formula 88
ISI 351
Iterated expectation 211
Jacobian 114
Joint distribution 122
Jointly Gaussian 153
Kronecker delta response 102 408
Laplace transform 151
Laplacian 428
Law of Large Numbers 187 190
Lebesgue integral 423
Linear 406
Linear models 348
logistic 428
MAP 136
MAP estimation 147
Mapping 401
Marginal pmf 91
Markov chain 162
Markov inequality 242
Markov process 162 165 167
Mass 11
Matrix 403
Maximum a posteriori 136
Maximum a posteriori estimation 147
Maximum Likelihood Estimation 147
Mean 47 57 190
Mean function 158
Mean squared error 216 218
Mean vector 206
Mean, conditional 142
Measurable 98
Measurable space 25
Measure probability 42
Measure theory 11
Memoryless 159
Metric 78
Minimum distance 145
Mixture 69 375
ML estimator 147
MMSE 217
MODULO 2
Modulo, arithmetic 134
moment 47 57
Moment generating function 198
Moment, centralized 194
Moment, second 206
Moments 194
Monotone Convergence Theorem 202
Moving Average 275 295 344
Moving average filter 344
Moving-average random process 348
MSE 216
Mutually exclusive 394
Mutually independent 94
Nested expectation 211
Noise, white 302
Noisy channel 135
Nonempty 390
Nonnegative definite 405
numeric 390
One-sided 29 405
One-step prediction 221
One-to-one 402
Onto 402
Operation 146
Orthogonal 230
Orthogonality principle 226 230 231
Outer product 404
Paley — Wiener criteria 304
Partition 401
PDF 17 61
pdf, chi-squared 113
pdf, doubly exponential 62 428
pdf, elementary conditional 74
pdf, exponential 62 428
pdf, Gamma 428
pdf, Gaussian 62 428
pdf, k-dimensional 68
pdf, Laplacian 62 428
pdf, logistic 428
pdf, Rayleigh 428
pdf, uniform 17 61 428
pdf, Weibull 428
Phi function 64
pmf 20 48
pmf, binary 48 427
pmf, binomial 48 427
pmf, conditional 73 130
pmf, Poisson 428
pmf, product 124
pmf, uniform 48 427
pmf:geometric 427
Point 389
Pointwise convergence 240
poisson 428
Poisson counting process 350 362
Positive definite 405
Power set 35
Power spectral density 289 291
Prediction, one-step 221
Predictor, one-step 219
Predictor, optimal 218
Preimage 402
Probabilistic average 190
Probability density function 17 61
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