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| Авторизация |
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| Kay S.M. — Intuitive Probability and Random Processes using MATLAB |
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| Предметный указатель |
Functions, even 334 368 787
Functions, hermitian 650
Functions, monotone 337
Functions, odd 368 787
Fundamental theorem of calculus 310 786
Gamma function 300
Gamma PDF 300
Gaussian mixture PDF 332 371
Gaussian PDF 5 20 296 459
Gaussian random process, definition 677
Gaussian random process, linear filtering of 682 (see also “Bandpass random process”)
Gaussian random variable 296
Geometric probability law (mass function) 91 113 720
Geometric series 47 785
histogram 14
Homogeneous transition probabilities 745
Huffman code 156
Hypergeometric probability law (mass function) 63
IID see “Independent and identically distributed”
IIR see “Infinite impulse response filter”
Image coding 272
Image signal processing 419
Importance sampling 364
Impossible event 44
Impulse (discrete-time) 795
Impulse response 599 801 807
Impulses for continuous-time see “Dirac delta function”
In-phase component 693
Increment of random process for Poisson random process 714
Increment of random process for Wiener random process 679 687
Increment of random process, definition 526
Increment of random process, independent 526
Increment of random process, stationary 526
Independent and identically, distributed 466 678
Independent events 78 83
Independent increments 526
Independent random variables, definition 24 179
Independent random variables, factorization of CDF 392
Independent random variables, factorization of characteristic function 282 468
Independent random variables, factorization of PDF 392 462
Independent random variables, factorization of PMF 179 224
Independent random variables, functions of 199
Independent random variables, transforming Gaussian random variables 410
Independent subexperiments 90
Indicator random variable 353
Induction, proof by 783
Infinite impulse response filter 803
Infinite set 43
Inner product 791 798
Integration by parts 368 787
Integration using approximating sum 12 786
Interarrival times of Poisson process 718
interference suppression 624
Interpolation 611
Intersection of sets 39
Inverse probability integral transformation 324
Inverse Q function 308
Irreducible Markov chain 756
Joint CDF, computing probability from 391
Joint CDF, continuous-time random variables 389
Joint CDF, discrete-time random variables 177
Joint moments 189 192 266 412
Joint PDF from joint CDF 391
Joint PDF, bivariate Gaussian 385
Joint PDF, definition 381 458
Joint PMF, definition 171
Joint PMF, estimation of 202
Joint probability 76
Joint sample space 170
Jointly distributed random variables 170 379
Jointly WSS 642
Karhunen — Loeve transform 273
Laplacian PDF 298
Law of Averages see “Law of large numbers”
Law of Large Numbers 491
Least squares 538 546
Leibnitz rule 335 787
Line fitting 538
Linear prediction equations 618 (see also “Prediction”)
Linear Predictive Coding 628
Linear shift invariant system, definition 599 800
Linear shift invariant system, described by difference equation 605 802
Linear shift invariant system, effect on WSS random process 602 654
Linear systems see “Appendix D”
Linear time invariant system, definition 623 807
Linear time invariant system, effect on WSS random process 624
Linear transformation of Gaussian random variable 314
Linear transformation of Gaussian random vector 399 408 464
Linear transformation, joint PDF 399
Lowpass filter see “Filtering”
Lowpass random process 693
LPC see “Linear predictive coding”
LSI see “Linear shift invariant system”
LTI see “Linear time invariant system”
MA see “Moving average”
Magnitude response of linear system 802 808
Mappings, many-to-one 108
Mappings, one-to-one 108
Marginal CDF 392
Marginal characteristic function 265
Marginal PDF 387 441 461
Marginal pmf 174 224 249
Marginal probability 76
Markov chain 96 742
Markov property 267 735
Markov random process 715 739
Markov sequence 95
Markov state probability 742
MATLAB overview 31
MATLAB programs, AR and periodogram, spectral estimators 629
MATLAB programs, averaged periodogram, spectral estimator 580
MATLAB programs, calculation of inverse Q function 341
MATLAB programs, calculation of Q function 341
MATLAB programs, calculation of tail probability 366
MATLAB programs, cross-correlation estimator 662
MATLAB programs, decorrelation of random vector 271
MATLAB programs, demonstration of central limit theorem 511
MATLAB programs, estimated mean 22
MATLAB programs, estimated mean of squared Gaussian random variable 23
MATLAB programs, estimated PDF 21
MATLAB programs, estimated probability 22
MATLAB programs, estimated probability of error in digital communication system 27
MATLAB programs, estimation of ACS of AR, random process 578
MATLAB programs, estimation of PDF using histogram 328
MATLAB programs, general program for discrete random variable generation 165
MATLAB programs, generation of AR random process 559
MATLAB programs, generation of discrete random variable 122
MATLAB programs, generation of discrete random vector using conditioning 236
MATLAB programs, generation of Gaussian noise 18
MATLAB programs, generation of Gaussian random vector and estimation of mean and covariance 418
MATLAB programs, generation of Gaussian random vector using Cholesky decomposition 476
MATLAB programs, generation of Gaussian random vector using conditioning 448
MATLAB programs, generation of MA random process 529
MATLAB programs, generation of multiple discrete random variables 201
MATLAB programs, line fitting of summer rainfall 541
MATLAB programs, Poisson random process simulation 727
MATLAB programs, reverberation simulation 709
MATLAB programs, reverberation spectral estimation 706
MATLAB programs, scatter diagram for randomly phased sinusoid 537
MATLAB programs, Sierpinski triangle 766
MATLAB programs, simulation of birthday problem 59
MATLAB programs, simulation of die experiment (dependent Bernoulli trials) 232
MATLAB programs, simulation of heads for four coin tosses 7
MATLAB programs, simulation of nonstationary random processes 524
MATLAB programs, simulation of repeated coin tossing experiment 290
MATLAB programs, simulation of three random outcomes 18
MATLAB programs, three-state Markov chain simulation 764
MATLAB programs, tutorial MATLAB program 35
MATLAB programs, Wiener smoother 615
Matrix, autocorrelation 561
| Matrix, cofactor 790
Matrix, conformable 789
Matrix, determinant 790 792
Matrix, diagonal 791
Matrix, doubly stochastic 764 773
Matrix, eigenanalysis 793
Matrix, inversion, definition 790
Matrix, inversion, formula 792 794
Matrix, irreducible 756
Matrix, minor 790
Matrix, modal 261
Matrix, orthogonal 261 282 791
Matrix, partitioned 791 792
Matrix, positive definite (sernidefinite) 259 280 790 793
Matrix, rotation 264 282 430
Matrix, square 790
Matrix, stochastic 756
Matrix, symmetric 790
Matrix, Toeplitz 623
Matrix, transpose 790 792
Mean function 533 581
Mean of random variable see “Expected value”
Mean recurrence time 761
Mean sequence 533
Mean square error, definition 142 193 208 471
Mean square error, estimator 194 (see also “Prediction”)
Median 333 450
Memory less property of Poisson process 720
Mixed random variables 317 354
MODE 369
Modulation property of Fourier transform 797 806
Moments, central vs.noncentral 146 358
Moments, definition 146 355 467
Moments, existence of 161
Moments, exponential PDF 357 359
Moments, from characteristic function 149 199
Moments, geometrical PMF 149
Moments, multivariate Gaussian 468 684
Moments, table of 145 355
Monotonically increasing function 337
Monte Carlo method 13 365
Monty Hall problem 81
Moving average, definition 528 681
Moving average, general form 544
Moving average, miscellaneous 534 557 564 606 621 651 678 697
MSE see “Mean square error”
Multinomial coefficient 93 103
Multinomial probability law (mass function) 93 249
Multinomial theorem 249 278
Multipath fading see “Rayleigh fading sinusoid”
Mutually exclusive events 44 84
n-step transition probability matrix 748
Narrowband representation see “Bandpass random process”
Nonstationarity 526 689 711 746
normal see “Gaussian”
Notational conventions 777
Null set see “Empty set”
Nyquist rate sampling 584
Odd function 368 787 805
Odd sequence 796
Odds ratio 87 97
Opinion polling 503
Optical Character Recognition 419
Orthogonality 791 720
Orthogonality principle for linear prediction 474
Orthogonality principle, definition 474
Orthogonality principle, geometric interpretation 474 482
Outcome 38 44 518
Outer product 792
Parseval’s theorem 797 806
Partitioning of set 41
Pascal triangle 12
Pattern recognition 421
PDF see “Probability density function”
Periodic random process 591
Periodogram 568 (see also “Averaged periodogram”)
permutations 57
Phase of random process 569
Phase response of linear system 802 808
Phase shift keying 24
pmf see “Probability mass function”
Poisson counting random process 126 711
Poisson probability law (mass function) 113
Poisson random process 711
Poles of linear system 803
Positive semidefinite sequence 562
Posterior PMF 239
Posterior probability 87
Power (average) from PSD 575
Power (average) of random variable 553
Power spectral density at output of LSI system 602
Power spectral density at output of nonlinear system 685
Power spectral density of thermal noise 583
Power spectral density, AR random process 572
Power spectral density, continuous-time definition 582
Power spectral density, discrete-time definition 569 571
Power spectral density, estimation of 568 579
Power spectral density, MATLAB code for estimation 580
Power spectral density, one-sided version 576
Power spectral density, physical interpretation 608
Power spectral density, properties 573
Power spectral density, used for physical modeling 587 628
Prediction for AR random process 618 634
Prediction for bivariate Gaussian 413 447
Prediction for MA random process 621 (see also “Line fitting”)
Prediction of sinusoid 544 634
Prediction of WSS random process 618 622
Prediction, definition 142 471
Prediction, L-step for WSS random process 611
Prediction, linear 192 413 471
Prediction, mean square error 142 208 276
Prediction, nonlinear 195 245 447 454
Prior PMF 238
Prior probability 80 87
Probability calculations via, conditioning 444
Probability density function from CDF 310
Probability density function of mixed random variables 317 354
Probability density function, approximating by PMF 288
Probability density function, Cauchy from ratio of Gaussians 402
Probability density function, Cauchy, definition 299
Probability density function, chi-squared 302
Probability density function, conditional 437
Probability density function, definition 6 20 289 381 458
Probability density function, Erlang 302
Probability density function, estimation of 14 19
Probability density function, exponential 293 296 302
Probability density function, gamma 300
Probability density function, Gaussian mixture 332 371
Probability density function, Gaussian, bivariate 401
Probability density function, Gaussian, multivariate 459
Probability density function, Gaussian, scalar 296
Probability density function, Laplacian 298
Probability density function, mass analogy 292
Probability density function, normal see “Gaussian”
Probability density function, properties 293 458
Probability density function, Rayleigh from square root of Gaussians 403 690
Probability density function, Rayleigh, definition 302
Probability density function, table of 355
Probability density function, uniform from angle of Gaussians 403 690
Probability density function, uniform, definition 290 295
Probability function 44
Probability integral transformation 324
Probability mass function, Bernoulli 111
Probability mass function, Binomial 112
Probability mass function, definition 109 171
Probability mass function, estimation of 122 202
Probability mass function, Geometric 113
Probability mass function, mass analogy 130
Probability mass function, Poisson 113
Probability mass function, table of 145
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