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Kay S.M. Intuitive Probability and Random Processes using MATLAB
Kay S.M.  Intuitive Probability and Random Processes using MATLAB









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: Intuitive Probability and Random Processes using MATLAB

: Kay S.M.

:

This book is an introduction to probability and random processes that merges theory with practice. Based on the author's belief that only "hands on" experience with the material can promote intuitive understanding the approach is to motivate the need for theory using MATLAB examples, followed by theory and analysis, and finally descriptions of "real-world" examples to acquaint the reader with a wide variety of applications.


: en

: /

:

ed2k: ed2k stats

: 1st edition

: 2005

: 833

: 14.05.2008

: | | ID
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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
Booles 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 Morgans 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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