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