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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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