Peebles P.Z. — Probability, random variables, and random signal principles :: Электронная библиотека попечительского совета мехмата МГУ

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Peebles P.Z. — Probability, random variables, and random signal principles

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Название: Probability, random variables, and random signal principles

Автор: Peebles P.Z.

Аннотация:

This concise introduction to probability theory carries on the success of previous editions, offering readers a logical, well-organized look at the fundamental of the subject — includes applications that strengthen engineers' grasp of probability concepts.

Язык:

Рубрика: Математика/Вероятность/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 1987

Количество страниц: 349

Добавлена в каталог: 05.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

A posteriori probability      18
a priori probability      18
Algebra of sets      7
Ambiguity function      272
Amplitude modulation (AM)      192 275—279
Antenna temperature      231
Aresine density      84 333
Associative law of sets      7
Autocorrelation function: at product device output      191
Autocorrelation function: bound on      153
Autocorrelation function: defined      149 152—154
Autocorrelation function: derivatives of      203 246
Autocorrelation function: Fourier transform of      177 180 193
Autocorrelation function: Fourier transform of time average of      177 180
Autocorrelation function: measurement of      156—158
Autocorrelation function: of complex process      160—161 193
Autocorrelation function: of derivative of a process      166 246
Autocorrelation function: of linear system response      212—213
Autocorrelation function: of stationary process      149
Autocorrelation function: of wide-sense stationary process      150 153
Autocorrelation function: properties of      153
Autocorrelation function: relationship to power spectrum      177 179—181 191
Autocorrelation function: time      151
Autocorrelation function: time average of      177 179—180
Autocovariance function: defined      155 160
Autocovariance function: Fourier transform of      196
Autocovariance function: of complex process      160
Autocovariance function: of wide-sense stationary process      156 158
Available power gain      232
Average effective noise temperature      237
Average effective source temperature      237
Average operating noise figure      236
Average standard noise figure      236
Axioms of probability      10
Band-limited random process      219
Band-limited random process, properties of      221—223 224—226
Band-limited while noise      188
Bandpass random process      219
Bandwidth: noise      210 217—218 238
Bandwidth: of a power spectrum      177—179
Bandwidth: rms      117—179 198 201
Bayes' theorem      16
Bayes, Thomas      16n.
Bernoulli density      331
Bernoulli trials      25
Bernoulli, Jacob      25n.
Bessel function      299 331
Beta density      333
Binary communication system      17
Binary process, semirandom      162
Binary symmetric channel      17
Binomial coefficient      26 33
Binomial density function      46 332
Binomial density function, characteristic function of      85
Binomial density function, mean of      81
Binomial density function, variance of      81
Binomial distribution function      46
Bivariate gaussian density      124 335
Boltzmann's constant      227
Boltzmann, Ludwig      227n.
Bound(s): on autocorrelation function      153
Bound(s): on cross-correlation function      154 155
Bound(s): on linear system response      210
Bounded variation      310n. 321n.
Butterworth filter      241
Cartesian product space      22n.
Cauchy density function      61 333
Cauchy distribution function      62
Cauchy random variable      61
Cauchy, Augustin Louis      61n.
Causal system      210
Central limit theorem      105—108
Central moments      70 82 120
Central moments, related to moments about origin      82
Certain event      10
Channel      17 276 281
Channel, binary symetric      17
Characteristic function: defined      72 122
Characteristic function: for several random variables      124
Characteristic function: for two random variables      122
Characteristic function: joint      122—124 138
Characteristic function: marginal      123
Characteristic function: moment generating properly of      72 123—124
Characteristic function: of binomial density      85
Characteristic function: of Erlang random variable      85
Characteristic function: of exponential random variable      72 73
Characteristic function: of gaussian random variable(s)      83 138
Characteristic function: of Poisson random variable      85
Chebychev's inequality      85
Chebychev, Pafnufy L.      85n.
Chi-square density      85 331 334
Class of sets      3
Classification of process      144 146
Coefficient of skewness      71
Colored noise      190
Combined experiment      22
Combined sample space      22
Communication system(s): amplitude modulation (AM)      275—279
Communication system(s): binary      17
Communication system(s): frequency allocations      275—276 280
Communication system(s): frequency modulation (FM)      280 284
Communication system(s): three-symbol      33
Commutative law of sets      7
Complement of set      6
Complex random process      160—161; see also Random process
Complex random variable      133
Conditional density function      52 62
Conditional density function with interval conditioning      99
Conditional density function with point conditioning      96—99
Conditional density function, properties of      53
Conditional distribution function      52 62 96
Conditional distribution function with interval conditioning      99
Conditional distribution function with point conditioning      96—99
Conditional distribution function, properties of      52
Conditional expected value      69 139
Conditional probability      13
Conditioning event      55—57
Conditioning event, interval      99
Conditioning event, point      96—96
Continious random sequence      146
Continous random variable      37
Continuous random process      145
Convolution integral      103 207 223
Convolution of density functions      103 105
Correlation coefficient      121 136
Correlation functions: autocorrelation      149 152 154 160—161 212—213
Correlation functions: autocovariance      155—156 160—161
Correlation functions: cross-correlation      150 154 213—214
Correlation functions: cross-covariance      156
Correlation functions: of derivative of a process      166 246
Correlation functions: time autocorrelation      151
Correlation functions: time cross-correlation      152 See
Correlation integral      268
Correlation receiver      269
Correlation: of independent random variables      119 134
Correlation: of orthogonal random variables      119 134
Correlation: of random variables      119 134
Correlation: of unconelated random variables      119 134
Countable set      3
Countably infinite set      3
Covariance functions      see Correlation functions
Covariance matrix      127
Covariance matrix after linear transformation      132
Covariance: of independent random variables      121
Covariance: of orthogonal random variables      121
Covariance: of random variables      121 134
Covariance: of uncorrelated random variables      121 134
Crest-factor      280 306
Cross power      181
Cross-correlation function(s): bounds on      154 155

Cross-correlation function(s): defined      150 154
Cross-correlation function(s): Fourier transform of      184 185—186 193
Cross-correlation function(s): measurement of      156—158
Cross-correlation function(s): of complex process      160—161 193
Cross-correlation function(s): of derivative of process      166 203 246
Cross-correlation function(s): of independent processes      154
Cross-correlation function(s): of jointly wide-sense stationary processes      150 154
Cross-correlation function(s): of orthogonal processes      154
Cross-correlation function(s): of response of linear system      213—214
Cross-correlation function(s): properties of      154
Cross-correlation function(s): real and imaginary parts of      199
Cross-correlation function(s): relationship to cross-power spectrum      184 185—186 193
Cross-correlation function(s): time      152
Cross-correlation function(s): time average of      184 185—186
Cross-covariance function: defined      156
Cross-covariance function: of complex processes      160—161
Cross-covariance function: of independent processes      156
Cross-covariance function: of uncorrelated processes      156
Cross-covariance function: of wide-sense stationary processes      156
Cross-power density spectrum: defined      183
Cross-power density spectrum: of complex processes      193
Cross-power density spectrum: of linear system      217
Cross-power density spectrum: properties of      184
Cross-power density spectrum: real and imaginary parts of      199
Cross-power density spectrum: relationship to cross-correlation function      184 185—186 193
Cross-power spectrum      see Cross-power density spectrum
Crossover frequency      308
Cumulative probability distribution function      see Probability distribution function
Damping factor      295
De Morgan's laws      7 32
de Morgan, Augustus      7n.
Decibels      240n.
Delta function      see Impulse function
Density function      see Probability density function
Derivative of random process      166 203
Derivative of random process, power spectrum of      177
Detection probability      304—305
Deterministic random process      147
Deterministic signal      173
Difference of sets      5
Dirichlet conditions      321n.
Dirichlet, Peter Gustav Lejeune      321n.
Discrete random process      145
Discrete random sequence      146
Discrete random variable      37 79
Disjoint sets      3
Distribution function      see Probability distribution function
Distributive law of sets      7
Domain      58
Duality principle      8
Effective noise temperature      229 233 237
Efficiency      279 305—306
Elementary event      12
Elements of a set      3
Empty set      3
Ensemble      143
Ensemble average      143
Ensemble member      143
Envelope detector      278
Equal sets      5
Ergodic random process      152 157n.
Ergodic theorem      152
Erlang density      334
Erlang random variable      85
Erlang, A.K.      85n.
Event(s): certain      10
Event(s): defined      9
Event(s): elementary      12
Event(s): impossible      10
Event(s): joint      89
Event(s): mutually exclusive      9
Event(s): on combined sample space      23—24
Event(s): pairwise independence of      19
Event(s): probability of      10
Event(s): statistically independent      18—22
Excess available noise power      233
Expectation      see Expected value
Expected value (expectation): conditional      69 139
Expected value (expectation): of a function of a random variable      68 133
Expected value (expectation): of a function of several random variables      117—119
Expected value (expectation): of a random variable      67—68 133
Expected value (expectation): of a sum of random variables      118
Expected value (expectation): of random process      143 153 160
Experiment(s)      8
Experiment(s), combined      22
Experiment(s), independent      25
Experiment(s), mathematical definition of      8 11—12
Exponential density function      49 68 70 71 72—74 334
Exponential distribution function      49 334
False alarm      302
Filter (system): Butterworth      243
Filter (system): gaussian      241
Filter (system): idealized      209—210
Filter (system): matched      258—262
Filter (system): prediction      263
Filter (system): smoothing      263
Filter (system): Wiener      262—266
Finite set      3
First-order stationary random process      148
Fourier series: coefficients      324 325
Fourier series: defined      324
Fourier transform of      324 325
Fourier transform(s): defined      72 173 320
Fourier transform(s): existence      321
Fourier transform(s): inverse      72 173 320
Fourier transform(s): multidimensional      323
Fourier transform(s): of autocorrelation fund ion      177 180 193
Fourier transform(s): of cross-correlation function      184 185—186 193
Fourier transform(s): of time-averaged autocorrelation function      177
Fourier transform(s): of time-averaged cross-correlation function      184
Fourier transform(s): properties of      321—323
Fourier transform(s): table of pairs of      329
Fourier transform(s): uniqueness      161
Fourier, Barton Jean Baptiste Joseph      320n.
Frequency modulation (FM)      280—284
Frequency-domain analysis      172
Fresnel integrals      273
Gamma density      335
Gamma function      85 330 331
Gauss, Johann Friedrich Carl      43n.
Gaussian density function: conditional      112 128
Gaussian density function: marginal      125 128
Gaussian density function: mean value of      81 124
Gaussian density function: N-dimensional (N-variate)      127 128
Gaussian density function: of one random variable      43 60 61 335
Gaussian density function: two-dimensional (bivariate)      112 124 335
Gaussian density function: variance of      81 124 336
Gaussian distribution function: of one random variable      44 335
Gaussian distribution function: table of      315
Gaussian filler      241
Gaussian random process      156 158—160
Gaussian random process, variance estimate of      167
Gaussian random variable(s): characteristic function of      83 138
Gaussian random variable(s): conditional density function of      128
Gaussian random variable(s): defined      43 124 127
Gaussian random variable(s): linear transformation of      77 130—133
Gaussian random variable(s): marginal density function of      125 128
Gaussian random variable(s): mean value of      81 124
Gaussian random variable(s): moment generating function of      83
Gaussian random variable(s): properties of      128
Gaussian random variable(s): variance of      81 124 336
Idealized system      209—210
Impossible event      10
Impulse function: defined      41 31—0312
Impulse function: limiting forms of      176 195
Impulse function: N-dimensional      311
Impulse function: relationship to unit-step function      41 311 312
Impulse function: two-dimensional      311—312
Impulse response of linear system      206 207
Incomplete beta function      331

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