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