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Gray R.M., Davisson L.D. — Introduction to statistical signal processing
Gray R.M., Davisson L.D. — Introduction to statistical signal processing

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Название: Introduction to statistical signal processing

Авторы: Gray R.M., Davisson L.D.

Аннотация:

This volume describes the essential tools and techniques of statistical signal processing. At every stage, theoretical ideas are linked to specific applications in communications and signal processing. The book begins with an overview of basic probability, random objects, expectation, and second order moment theory followed by a wide variety of examples of the most popular random process models and their basic uses and properties. Specific applications to the analysis of random signals and systems for communicating, estimating, detecting, modulating, and other processing of signals are interspersed throughout the text.


Язык: en

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 444

Добавлена в каталог: 03.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\delta$ response      102
$\Phi$ 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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