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

Incomplete gamma function      330 331
Incremental available power      227
Incremental noise power      227
Independent events      18—22
Independent experiments      25
Independent random processes      148
Independent random variables      100—102 133—134
Independent random variables, joint characteristic function of      122—124 138
Infinite set      3
Integrals: Fresnel      273
Integrals: table of definite      318—319
Integrals: table of indefinite      316—318
Integrator      157
Intersection of sets      6
Interval conditioning      99
Inverse Fourier transform      see Fourier transform
j      60n.
Jacobi, Karl Gustav Jakob      129n.
Jacobian      129
Joint central moments      120—122
Joint central moments of two discrete random variables      136
Joint characteristic function      122—124
Joint characteristic function of independent random variables      138
Joint characteristic function of two gaussian random variables      83 138
Joint event      89
Joint moments      119—120
Joint moments of two discrete random variables      136
Joint probability      13
Joint probability density function      see Probability density function
Joint probability distribution function      see Probability distribution funclion
Joint sample space      88
Jointly ergodic random processes      152 157n.
Jointly gaussian random processes      156 160
Jointly wide-sense stationary random processes      150 160—161 213
Khinchin, A.I.      180
Laplace density function      59 336
Laplace transform      173
Laplace, Marquis Pierre Simon de      59n.
Leibniz's rule      16
Leibniz, Gottfried Wilhelm von      76n
Likelihood      9
Linear system: causal      210
Linear system: cross-correlation function      213—214
Linear system: cross-power spectrums      217
Linear system: defined      206
Linear system: idealized      209—210
Linear system: impulse response      206 207 210
Linear system: noise temperature      239
Linear system: optimum      257
Linear system: output autocorrelation function      212—213
Linear system: output mean value      211
Linear system: output mean-squared value      212
Linear system: output power      212 216
Linear system: output power spectrum      215
Linear system: physically realizable      210
Linear system: response to deterministic signal      206—209
Linear system: response to random signal      211
Linear system: stable      210
Linear system: time-invariant      207
Linear system: transfer function      208
Linear system: while noise evaluation of      214—215
liquid helium      200
Log-normal density function      62 86 336
Log-normal distribution function      62 336
Mapping      35
Marcum's Q-function      305 331
Marginal characteristic function      123
Marginal density function      see Probability density function
Marginal distribution function      see Probability distribution function
Maser      188n. 200
Matched filler      258
Matched filler for colored noise      259—260
Matched filler for rectangular pulse      261—262
Matched filler for white noise      260—262
Matched filler, impulse response      260 261 267
Matched filler, maximum signal-to-noise ratio of      260 268
Matched filler, output signal from      268
Matched filler, transfer function      260
Matrix, covariance      127
Mean (expected) value: conditional      69 139
Mean (expected) value: estimate of      167
Mean (expected) value: from autocorrelation function      153
Mean (expected) value: of function of .several random variables      117—119
Mean (expected) value: of function of a random variable      68 113
Mean (expected) value: of process sample function      181
Mean (expected) value: of random process derivative      160
Mean (expected) value: of random process(es)      141 160
Mean (expected) value: of random variable      67—68 133
Mean (expected) value: of sum of random variables      118
Mean (expected) value: of system response      211
Mean frequency      178
Mean time between failures (MTBF)      64
Mean-squared error      263—266
Measurement of correlation functions      156—158
Median of random variable      61
Mixed random variable      37
Mode of random variable      61
Modulation index      306
Moment generating function      73
Moment generating function of gaussian random variable      83
Moments: about origin      69 82 119—120
Moments: central      70 82 120
Moments: from characteristic function      72 123—124
Moments: from moment generating function      73
Moments: interrelationships      82
Moments: joint      119—122
Moments: of two discrete random variables      136
Monotonic transformations: decreasing      75 76
Monotonic transformations: increasing      75—76
Mutually exclusive events      9
Mutually exclusive sets      3
N-order stationary random process      151
Narrowband gaussian process      220
Narrowband random process      220
Natural frequency      295
Natural numbers      80
Noise      1
Noise bandwidth      210 217—218 238
Noise figure: average      236
Noise figure: average operating      236
Noise figure: average standard      216
Noise figure: average system operating:      240
Noise figure: incremental      244
Noise figure: of attenuator      238
Noise figure: operating spot      235 249
Noise figure: spot      234—235
Noise figure: standard spot      235 250
Noise in control system      285—288
Noise in phase-locked loop      288—295
Noise performance: of amplitude modulation system      278—279
Noise performance: of frequency modulation system      281—284
Noise performance: of phase-locked loop      292—295
Noise performance: of radar      301—305
Noise temperature: average      237—238
Noise temperature: average effective input      237
Noise temperature: average effective source      237
Noise temperature: effective      228
Noise temperature: effective input      233
Noise temperature: of antenna      231
Noise temperature: standard      235
Noise temperature: system      239
Noise, arbitrary source of      228
Noise, colored      190
Noise, resistive source of      227
Noise, thermal      187 227
Noise, types of      226n.
Noise, while      187
Nondeterministic random process      147
Nonstationary random process      147
Normal density function      see Gaussian density function

Normal distribution function      see Gaussian distribution function
Normalized second-order moment      121
Null set      3
Open-loop transfer function      285
Operating spot noise figure      235 249
Operator      206
Order of moment      119 120
Orthogonal random process      154 161
Orthogonal random variables      119 134
Outcome of experiment      8
Overmodulation      278n. 306
Parseval's theorem      323
Parseval, M.A.      323n.
Pascal density      332
Pascal, Blaise      332.
Phase detector      290
Point conditioning      96—99
Poisson density function      47 85 119
Poisson density function, mean of      81 332
Poisson density function, variance of      81 332
Poisson random variable      47 140
Poisson, Simeon Denis      47n.
power density      see Power density spectrum
Power density spectrum      153 173
Power density spectrum of complex process      193
Power density spectrum of derivative of process      177
Power density spectrum, bandwidth of      177—179
Power density spectrum, defined      75
Power density spectrum, inverse Fourier transform of      177 180
Power density spectrum, of output of linear system      215
Power density spectrum, of product device output      191
Power density spectrum, properties of      176—177
Power density spectrum, relationship of autocorrelation function      177 179—181
Power density spectrum, relationship to aulocovariance function      196
Power gain, available      232
Power spectral density      173n.
Power spectrum      see Power density spectrum
Power transfer function      215
Power: from autocorrelation function      153
Power: from power density spectrum      175
Power: from second moment of process      175
Power: in a random process      153 173 175
Power: in response of linear system      212 216
Power: incremental available      227
Prediction filter      263
probability      9
Probability density function: aresine      84 333
Probability density function: Bernoulli      331
Probability density function: beta      333
Probability density function: binomial      46 81 332
Probability density function: Cauchy      61 333
Probability density function: chi-square      85 331 334
Probability density function: conditional      52 96—99
Probability density function: defined      40 93 148
Probability density function: Erlang      334
Probability density function: existence      40
Probability density function: exponential      19 334
Probability density function: gamma      335
Probability density function: gaussian      43 60 61 112 124—128 335
Probability density function: joint      93
Probability density function: Laplace      59 81 336
Probability density function: log-normal      62 86 336
Probability density function: marginal      95 96
Probability density function: normal      43n.
Probability density function: of discrete random variable(s)      41 94
Probability density function: of N random variables      94
Probability density function: of random process(es)      148n.
Probability density function: of sum of random variables      102—105
Probability density function: of two random variables      93
Probability density function: Pascal      332
Probability density function: Poisson      47 85 332
Probability density function: properties of      42 53 94
Probability density function: Rayleigh      50 336
Probability density function: Rice      299 137
Probability density function: transformation of      74—80 128—133
Probability density function: triangular      43
Probability density function: uniform      48 337
Probability density function: Weihull      85 338
Probability distribution function: aresine      333
Probability distribution function: Bernoulli      331
Probability distribution function: beta      333
Probability distribution function: binomial      46 332
Probability distribution function: Cauchy      62 333
Probability distribution function: chi-square      334
Probability distribution function: conditional      52 62 96—99
Probability distribution function: defined      37 89 147—148
Probability distribution function: Erlang      334
Probability distribution function: exponential      49 334
Probability distribution function: gamma      335
Probability distribution function: gaussian      43—45 335
Probability distribution function: joint      89 90 148
Probability distribution function: Laplace, 336
Probability distribution function: log-normal      62 336
Probability distribution function: marginal      92 93
Probability distribution function: of discrete random variable(s)      38 90
Probability distribution function: of one random variable      37
Probability distribution function: of random process      147n. 147—148
Probability distribution function: of several random variables      90
Probability distribution function: of sum of random variables      102—105
Probability distribution function: of two random variables      89
Probability distribution function: Pascal      332
Probability distribution function: Poisson      47 332
Probability distribution function: properties of      37—38
Probability distribution function: Rayleigh      50 337
Probability distribution function: Rice      337
Probability distribution function: uniform      48 337
Probability distribution function: Weibull      338
Probability of detection      302 304—305
Probability of false alarm      302 303
Probability of miss      302
Probability, a posteriore      18
Probability, a priori      18
Probability, axioms of      10
Probability, conditional      13
Probability, defined      10
Probability, joint      13
Probability, total      15
Probability, transition      18
Process      see Random process
Product device      191—193
Product of sets      6
Product space, two-dimentional      88
Pulse repetition frequency (PRF)      301
Quantizer      58
Random point      88
Random process(es): autocorrelation function      149 152—154 160
Random process(es): autocovariance function      155 160
Random process(es): band-limited      219
Random process(es): bandpass      219
Random process(es): classified      144—146
Random process(es): complex      160—161
Random process(es): continuous      145
Random process(es): cross-correlation function      150 154 160—161
Random process(es): cross-covariance function      156 160—161
Random process(es): cross-power spectrum      182—185 193
Random process(es): defined      142 160
Random process(es): density function of      148
Random process(es): derivative of      166 246
Random process(es): deterministic      147
Random process(es): discrete      145
Random process(es): distribution function of      147—148
Random process(es): ergodic      152
Random process(es): estimate of      168
Random process(es): first-order stationary      148—149
Random process(es): gaussian      156 158—160
Random process(es): jointly ergodic      152 157n.
Random process(es): jointly wide-sense stationary      150 160—161 213
Random process(es): mean of      143 153 160
Random process(es): mean value estimate of      167
Random process(es): N-order stationary      151

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