Random Processes: Filtering, Estimation, and Detection

   INDEX

Additive white Gaussian noise (AWGN), 511–512

A posteriori density

maximum of, 160

mean of, 158

median of, 159

A posteriori probabilities, 424

Autoregressive (AR) process, 217, 221, 264

autocorrelation function

AR(1), 224

AR(2), 225

AR(p), 223

mean of AR(p), 221

steady state

autocorrelation function for

AR(1), 224, 267

AR(2), 226

AR(p), 223

mean for AR(1), 266

power spectral density for

AR(1), 267

AR(p), 268

transfer function, 264

variance of AR(p), 221

Autocorrelation function

complex random process, 184

real process, 184

Autocovariance function, 184

complex processes, 184

Autoregressive moving average (ARMA) process, 217, 264

autocorrelation ARMA(1, 1), 230

autocorrelation of, 227

definition, 226

mean of ARMA(p,q), 226

steady state

autocorrelation ARMA(1, 1), 269

mean ARMA(1, 1), 268

power spectral density ARMA(1, 1), 270

power spectral density ARMA(p,q), 270

variance, 231

transfer function, 264, 268

variance of ARMA(p,q), 227

Auxiliary random variable approach, 91

Bayes decision rule, 437–455

average cost, 437

M-class, 440–442, 445–446

Gaussian, 471

Gaussian—special cases, 471–475

MPE, 450

risk, 437

special cases 1 and 2, 451–452

two class, 437

general Gaussian, 467

general Gaussian performance, 467

zero-one cost assignment, 438

Bayes estimator, 157

absolute error cost, 157–158

examples, 160

squared error cost, 158

uniform cost, 157, 159

Bayes rule, 73

Bayes theorem, 24

Bernouilli trials, 9

approximations, 11–12

Bienayme inequality, 46

Bilinear system characterizations, ...