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| Kay S.M. — Intuitive Probability and Random Processes using MATLAB |
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| Предметный указатель |
Probability mass function, using Dirac delta function 324
Probability of error 26 80 308 446
Probability of interval 121 309
Probability of point 53 294
Probability of union 49
Probability, axioms 45
Probability, definition 44
Probability, monotonicity 50
Probability, zero probability events 384
Problem designations 8
Projection theorem 474
PSD see “Power spectral density”
Pseudorandom noise 629
PSK see “Phase shift keying”
Q function, approximation of 308
Q function, definition 306
Q function, evaluation of 341
Quadratic form 280 790
Quadrature component 693
Random number generator 7
Random process, Bernoulli 519
Random process, binomial counting 526
Random process, continuous-time/continuous-valued 520
Random process, continuous-time/discrete-valued 520
Random process, definition 518
Random process, discrete-time/continuous-valued 520
Random process, discrete-time/discrete-valued 520
Random process, Gaussian 677
Random process, infinite 520
Random process, Markov chain 744
Random process, nonstationary 526
Random process, Poisson 711
Random process, semi-infinite 520
Random process, stationary 524 551
Random process, sum 525 702
Random variable, continuous 287 377
Random variable, discrete 17 107 169
Random variable, mixed 317
Random vectors, definition 23 170 248 458
Random vectors, Gaussian 459
Random walk 267 522
Rayleigh fading sinusoid 403 689
Rayleigh PDF 302 403
Real-world examples, assessing health risks 202
Real-world examples, automobile traffic signal planning 728
Real-world examples, brain physiology research 663
Real-world examples, cluster recognition 97
Real-world examples, critical software testing 364
Real-world examples, data compression 155
Real-world examples, digital communications 24
Real-world examples, estimating fish populations 698
Real-world examples, image coding 272
Real-world examples, modeling human learning 237
Real-world examples, opinion polling 503
Real-world examples, optical character recognition 419
Real-world examples, quality control 64
Real-world examples, random vibration testing 586
Real-world examples, retirement planning 449
Real-world examples, servicing customers 124
Real-world examples, setting clipping levels 328
Real-world examples, signal detection 476
Real-world examples, speech synthesis 626
Real-world examples, statistical data analysis 538
Real-world examples, strange Markov chain dynamics 765
Realization 18 518
Relative frequency 1 7 19 759
Replica correlator 477
Reproducting property 184 279 414
Reverberation 674
Sample mean in detection 478
Sample mean, definition 21 154 279 466
Sample mean, law of large numbers 490 (see also “Ergodic”)
Sample space, continuous 52
Sample space, discrete 47 54
Sample space, general 44 518
Sample space, multiple random variables 248 458
Sample space, numerical vs.nonnumerical 106
Sample space, reduced 75
Sampling with (without replacement) 56
Scatter diagram 24 537
Sets 38
Sierpinski triangle 766
Signal detection 476
Signal-to-noise ratio 369
Signals see “Appendix D”
Simple set 39
Sinusoidal signal as random process, random amplitude 544
Sinusoidal signal as random process, random amplitude/phase 403 (see also “Rayleigh fading”)
Sinusoidal signal as random process, random phase 370 530 536 591 596
Sinusoidal signal, continuous-time definition 805
Sinusoidal signal, discrete-time definition 795
Sinusoidal signal, miscellaneous 557
Sinusoidal signal, PDF of random phase 530
Sinusoidal signal, prediction of 544
Sinusoidal signal, recursive generation of 544
Size of set 43
Smoothing, Wiener, definition 611
Smoothing, Wiener, MATLAB code for 615
SNR see “Signal-to-noise ratio”
Source encoding 155
Spectral estimation 568 579
Spectral factorization 696
Spectral representation theorem 569
| Speech synthesis 626
Stable linear system 801 807
Stable sequence 796
Standard bivariate Gaussian 385 394
Standard deviation 356 371
Standard normal random variable 296 305
Standardized random variable 195
Standardized sum 495
State 742
State occupation time 759
State probabilities 742
State probability diagram 95 742
State transition matrix 742
Stationarity for WSS random process 680
Stationarity, definition 524
Stationarity, relation to IID 524
Stationary increments 526
Stationary probabilities for Markov chain, computing 750 762 771
Stationary probabilities for Markov chain, definition 749 757
Steady-state probabilities see “Stationary probabilities for Markov chain”
Step function 805
Step sequence 795
Stirling’s formula 71
Subexperiments 89
Sum of Poisson random processes 733
Sum of random number of random variables 234 723
Sum of random processes 653
Sum of random variables of Gaussian random variables 414
Sum of random variables of Poisson random variables 279
Sum of random variables of uniform random variables 395
Sum of random variables, binomial from Bernoulli 254
Sum of random variables, finding PDF 397 470
Sum of random variables, finding PMF 254
Sum of random variables, finding variance 257
symbols 777
System function 600 604 681 801
Tail probability 305 (see also “Importance sampling”)
Taylor expansion 130 785
Temporal average 563
Temporal average for Markov chain 760
Total probability for PDFs 445
Total probability for PMFs 229
Total probability for probability of event 79
Transform coding 273
Transformations of continuous random variable 22 313 316
Transformations of discrete random variable 115
Transformations of multiple random variables 181 251 400 464
Transformations, general funcion of 464
Transformations, nonlinear-Gaussian random processes 684
Transformations, PDF of product 429
Transformations, PDF of quotient 402 429 445
Transformations, sum of random variables 184 397
Transformations, using CDF approach 317
Transformations, using conditioning approach 225
transforms see “Appendix D”
Trellis 96
Tuples 55
Uncorrelated random variables and independence 462
Uncorrelated random variables, definition 196
Uncorrelated WSS random processes 647
Uncountable set 43 285
Uniform PDF 290 295
Uniform PMF 145
union 39
Union bound see “Boole’s inequality”
Unit step function 320
Unit step sequence 183
Universal set 38
Variance of sum 188 257 465
Variance, conditional 230
Variance, definition 143 355
Variance, estimation of 154 364
Variance, function 533
Variance, properties 145
Variance, sequence 533
Variance, table of 145
Venn diagram 40
Vibration analysis 586
Waiting times see “Arrival times of Poisson process”
WGN see “White Gaussian noise”
White Gaussian noise, bandpass version 584 694
White Gaussian noise, continuous-time definition 686
White Gaussian noise, discrete-time definition 528
White Gaussian noise, miscellaneous 534 677
White Gaussian noise, obtaining discrete-time from continuous-time 583
White noise 556 569 571
Whitening (preemphasis) 661
Wide sense stationary, definition 550
Wide sense stationary, generating realization of 681
Wide sense stationary, jointly distributed 642
Wiener filtering, definition 609
Wiener filtering, filtering 609
Wiener filtering, interpolation 611
Wiener filtering, prediction 611
Wiener filtering, smoothing 611
Wiener random process, computer generation of realization 704
Wiener random process, continuous-time 687 703
Wiener random process, discrete-time 679
Wiener — Hopf equations 623
Wiener — Khinchine theorem 571
Wolfer sunspot data 548
WSS see “Wide sense stationary”
Yule — Walker equations 623
z-transform 800
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