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| Kay S.M. — Intuitive Probability and Random Processes using MATLAB |
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| Предметный указатель |
abbreviations 782
ACF see “Autocorrelation function”
ACS see “Autocorrelation sequence”
Affine transformation 313 400
ar see “Autoregressive”
ARMA see “Autoregressive moving average”
Arrival angle measurement 671
Arrival rate of Poisson process 713
Arrival times of Poisson process 721 734
Autocorrelation function, definition 581
Autocorrelation function, properties 581 624
Autocorrelation matrix 561
Autocorrelation method of LPC 628
Autocorrelation sequence for deterministic signal 798
Autocorrelation sequence, definition 552
Autocorrelation sequence, estimator 577 627
Autocorrelation sequence, LSI system output 602 604
Autocorrelation sequence, MATLAB code for estimation 578
Autocorrelation sequence, properties 553
Autoregressive for modeling of PSD 588 628
Autoregressive Moving Average 681
Autoregressive, autocorrelation sequence 560
Autoregressive, cross-correlation of filter input/output 668
Autoregressive, definition 558 633 681
Autoregressive, generation of realization 592 595
Autoregressive, linear prediction 618
Autoregressive, power spectral density 572
Auxiliary random variable 183 251 403
Average power 553 575 582
Average value see “Expected value”
Averaged periodogram, definition 579
Averaged periodogram, MATLAB code for 580
Averages, ensemble 563
Averages, temporal 563
Bandpass random process, definition 691
Bandpass random process, representation 692
Bandpass random process, “white” Gaussian noise 694
Bayes’ Theorem 86
Bayes’ theorem for conditional PDF 223
Bernoulli law of large numbers 490
Bernoulli probability law (mass function) 111
Bernoulli random process 517
Bernoulli sequence 90
Bernoulli trial, dependent 94
Bernoulli trial, independent 90
Bernoulli trial, Markov chain 739
Binomial coefficient see “Combinations”
Binomial counting random process 526
Binomial probability law (mass function), approximation by Gaussian 501
Binomial probability law (mass function), approximation by Poisson 113 152 712
Binomial probability law (mass function), definition 4 63 91 112
Binomial probability law (mass function), maximum value 129
Binomial theorem 11 68 71
Bins 21
Birthday problem 57
Bivariate Gaussian PDF, definition 401 408
Bivariate Gaussian PDF, standardized version 385
Bivariate PMF see “Joint PMF”
Body mass index 202
Boole’s inequality 52
Box — Mueller transform 431
Brownian motion see “Wiener random process”
Cartesian product of sets 89
Cauchy PDF 299 402
Cauchy — Schwarz inequality 197 213 645
Causal signal 796
Causal system 605 801 807
CCF see “Cross-correlation function”
CCS see “Cross-correlation sequence”
CDF see “Cumulative distribution function”
Central limit theorem, description 495 497 501
Central limit theorem, proof 513
Central limit theorem, used as justification for modeling 674
Central limit theorem, using to compute binomial probabilities 501
Central limit theorem, using to compute chi-squared probabilities 497
Central moments 146 190
Certain set 44
Chain rule (probability) 85 266
Chain rule for Markov chains 745
Channel delay measurement 658
Chapman — Kolmogorov equations 748
Characteristic function for multivariate Gaussian 481
Characteristic function, convergence of sequence 152 361
Characteristic function, finding moments from 149 199 266 468
Characteristic function, finding PDF from 361
Characteristic function, finding PMF from 185
Characteristic function, joint definition 198 265 414 467
Characteristic function, properties 151
Characteristic function, scalar definition 147 359
Characteristic function, table of 145 355
Chebyshev inequality 362
Chi-squared PDF 302 429 480 498 509
Cholesky decomposition 417 475
Clutter 674
Coherence function 649
Combinations 60
Combinatorics 54
Communications, channel modeling 104
Communications, error probability 308
Communications, model of link 81
Communications, phase shift keying 24
Complement set 39
Compound Poisson random process, characteristic function 724
Compound Poisson random process, definition 723
Compound Poisson random process, mean function 726
Compound Poisson random process, variance function 735
Computer data generation, AR random process 592 595 633
Computer data generation, bivariate Gaussian 416 448
Computer data generation, Cauchy 368
Computer data generation, conditioning approach 235 447
Computer data generation, continuous-time Wiener random process 704
Computer data generation, discrete random variables 122
Computer data generation, discrete random vectors 200
Computer data generation, exponential 366
Computer data generation, Gaussian 18 27 33 431
Computer data generation, Gaussian from sum of uniforms 481
Computer data generation, given covariance matrix 283
Computer data generation, Laplacian 326
Computer data generation, Markov chain 764
Computer data generation, multivariate Gaussian 475
Computer data generation, Poisson random process 727
Computer data generation, Uniform 26 33
Computer data generation, WSS with given PSD 696
Conditional expectation, definition 229 446
Conditional expectation, properties 233 447
Conditional mean see “Conditional expectation”
Conditional PDF of bivariate Gaussian 439
Conditional PDF, definition 437
Conditional PDF, properties 440
Conditional PMF and independence 224
Conditional PMF and Markov property 745
Conditional PMF, definition 218 266
Conditional PMF, properties 222
Conditional probability 75
Confidence interval 504
Continuity theorem for characteristic functions 152 361
Contours of constant PDF 382 386
Convergence in probability 491
Convergence of random variables 507
Convolution to compute PDF 493
Convolution to compute PMF 184
Convolution, integral 396 493 624 685 806
Convolution, MATLAB program to compute 511
Convolution, sum 200 599 798
Correlation and causality 197
Correlation coefficient for prediction 196
Correlation coefficient for random processes 555 649
Correlation coefficient for standard bivariate Gaussian 407
Correlation coefficient, definition 196
Correlation coefficient, estimation of 210
| Correlation of signals 798
Correlation time 695
Correlation, definition 196
Countable set 43
Countably infinite set 43
Counting methods 37 54
Covariance for bivariate Gaussian PDF 406
Covariance function 533
Covariance matrix for Gaussian PDF 408 459
Covariance matrix for uncorrelated random variables 259 465
Covariance matrix, definition 258 281
Covariance matrix, diagonalization 260
Covariance matrix, eigenanalysis 261 431
Covariance matrix, estimation of 270
Covariance matrix, properties 258 561
Covariance of independent random variables 191
Covariance sequence 533
Covariance, definition 188
Covariance, estimation of 211 545
Covariance, properties 208
CPSD see “Cross-power spectral density”
Cross-correlation function, definition 657
Cross-correlation function, properties 657
Cross-correlation sequence for deterministic signals 798
Cross-correlation sequence, definition 643
Cross-correlation sequence, estimation of 662
Cross-correlation sequence, MATLAB program for estimation 662
Cross-correlation sequence, properties 645
Cross-power spectral density at input/output of filter 654
Cross-power spectral density, continuous-time definition 657
Cross-power spectral density, discrete-time definition 647 648
Cross-power spectral density, properties 650
Cross-spectral matrix 669
CTCV see “Continuous-time/continuous-valued under random process”
CTDV see “Continous-time/discrete-valued under random process”
Cumulative distribution function, conditional 441 449
Cumulative distribution function, continuous random variable 303 389 463
Cumulative distribution function, discrete random variable 118 250
Cumulative distribution function, mixed random variable 319
D/A see “Digital-to-analog”
Data compression via Markov chain 767
Data compression via source encoding 155
Data generation see “Computer data generation”
DB see “Decibel”
dc see “Direct current”
de Morgan’s laws 42
Decibel 629
Decorrelation of random variables 208 260 410
Demodulation 705
DeMoivre — Laplace theorem 501
Dependent subexperiments 94
DFT see “Discrete Fourier transform”
Differencer 552 681
Digital-to-analog convertor 629
Dirac delta function 319 336 787 804
Direct current (DC level) signal 477 566
Discrete Fourier transform, definition 799
Discrete Fourier transform, to approximate inverse Fourier transform 616 799
Discrete Fourier transform, use in spectral analysis 580
Disjoint sets 41 44 67
Dow — Jones industrial average 517
DTCV see “Discrete-time/continuous-valued under random process”
DTDV see “Discrete-time/discrete-valued under random process”
Dyad see “Outer product”
Eigenanalysis (eigendecomposition), definition 261 793
Eigenanalysis (eigendecomposition), used to find powers of matrix 750
Eigenvalue/eigenvector 793
Empty set 38
Ensemble average for Markov chain 563
entropy 157 (see also “Real-world example-data compression”)
Envelope of random process 693 705
Ergodic, autocorrelation 577
Ergodic, definition 564
Ergodic, Markov chain 752 761
Ergodic, mean 564
Erlang PDF 302 721
Estimation, autocorrelation sequence 577
Estimation, autoregressive parameters 623
Estimation, CDF 123
Estimation, correlation coefficient 210
Estimation, covariance matrix 270
Estimation, cross-correlation sequence 662
Estimation, interval 20
Estimation, least squares 538 546
Estimation, mean 21 154 364
Estimation, moments 154 202
Estimation, PDF 14 19
Estimation, PMF 122 202
Estimation, power spectral density 568 579
Estimation, probability of error 27
Estimation, probability of heads 7 19
Estimation, variance 154 364
Even function 334 368 787 805
Even sequence 554 796
Events, definition 44
Events, impossible 44
Events, joint 76 458
Events, simple 44
Events, zero probability 48 53 384
Expected value and conditional expectation 230
Expected value for function of 140 187 351 405
Expected value from CDF 370
Expected value of conditional PDF 446
Expected value of conditional PMF 229
Expected value of product 187 405
Expected value of sum 187 405 465
Expected value, bounds on 368
Expected value, center of mass analogy 158 346
Expected value, estimation of 154 364
Expected value, matrix 260 281
Expected value, nonexistence of 139 159 348
Expected value, properties 159 160
Expected value, scalar 136 345
Expected value, table of 145 355
Expected value, using conditioning 234 447
Expected value, vector 255 459
Experiments, dependence of subexperiments 94
Experiments, description 1
Experiments, independence of subexperiments 89
Experiments, subexperiments 89
Exponential function as infinite series 785
Exponential function as limit 784
Exponential PDF 296 302
Extrapolation see “Prediction”
Factorial and Gamma function 301
Factorial, computing 72
Factorial, definition 4 57
Fast Fourier Transform 33 579 615
FFT see “Fast Fourier transform”
Filtering of jointly WSS random processes 653
Filtering, all-pole 627
Filtering, bandpass 694
Filtering, digital filter design 696
Filtering, interference rejection 624
Filtering, lowpass 25 659 804 808
Filtering, passband 656 804 808
Filtering, stopband 804 808
Filtering, Wiener 613
Finite dimensional distribution 523
Finite impulse response filter 600 803
Finite set 43
FIR see “Finite impulse response filter”
Fish population measurement 698
Forecasting see “Prediction”
Fourier transform, continuous-time Fourier transform, as narrowband filter 670
Fourier transform, continuous-time Fourier transform, definition 805
Fourier transform, continuous-time Fourier transform, table of 806
Fourier transform, discrete-time Fourier transform, definition 796 798
Fourier transform, discrete-time Fourier transform, table of 797
Frequency response 600 802 808
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