Probability and random processes : with applications to signal processing and communications / Scott L. Miller, Donald Childers.
Editor: Amsterdam : Elsevier Academic Press, c2004Descripción: xiii, 536 p. : il. ; 24 cmISBN: 0121726517Tema(s): Signal processing -- Mathematics | Probabilities | Stochastic processesOtra clasificación: 60-01 (60K30 62M15) Recursos en línea: Publisher description1 Introduction [1] 1.1 A Speech Recognition System [3] 1.2 A Radar System [4] 1.3 A Communication Network [5] 2 Introduction to Probability Theory [7] 2.1 Experiments, Sample Spaces, and Events [8] 2.2 Axioms of Probability [11] 2.3 Assigning Probabilities [14] 2.4 Joint and Conditional Probabilities [18] 2.5 Bayes's Theorem [22] 2.6 Independence [25] 2.7 Discrete Random Variables [28] 2.7.1 Bernoulli Random Variable [31] 2.7.2 Binomial Random Variable [32] 2.7.3 Poisson Random Variable [33] 2.7.4 Geometric Random Variable [34] 2.8 Engineering Application: An Optical Communication System [35] Exercises [38] MATLAB Exercises [45] 3 Random Variables, Distributions, and Density Functions [47] 3.1 The Cumulative Distribution Function [48] 3.2 The Probability Density Function [53] 3.3 The Gaussian Random Variable [57] 3.4 Other Important Random Variables [63] 3.4.1 Uniform Random Variable [63] 3.4.2 Exponential Random Variable [64] 3.4.3 Laplace Random Variable [65] 3.4.4 Gamma Random Variable [66] 3.4.5 Erlang Random Variable [67] 3.4.6 Chi-Squared Random Variable [67] 3.4.7 Rayleigh Random Variable [68] 3.4.8 Rician Random Variable [69] 3.4.9 Cauchy Random Variable [69] 3.5 Conditional Distribution and Density Functions [71] 3.6 Engineering Application: Reliability and Failure Rates [77] Exercises [82] MATLAB Exercises [86] 4 Operations on a Single Random Variable [87] 4.1 Expected Value of a Random Variable [87] 4.2 Expected Values of Functions of Random Variables [90] 4.3 Moments [91] 4.4 Central Moments [94] 4.5 Conditional Expected Values [98] 4.6 Transformations of Random Variables [100] 4.7 Characteristic Functions [108] 4.8 Probability Generating Functions [114] 4.9 Moment Generating Functions [117] 4.10 Evaluating Tail Probabilities [119] 4.11 Engineering Application: Scalar Quantization [126] 4.12 Engineering Application: Entropy and Source Coding [134] Exercises [138] MATLAB Exercises [145] 5 Pairs of Random Variables [147] 5.1 Joint Cumulative Distribution Functions [148] 5.2 Joint Probability Density Functions [151] 5.3 Joint Probability Mass Functions [157] 5.4 Conditional Distribution, Density, and Mass Functions [159] 5.5 Expected Values Involving Pairs of Random Variables [163] 5.6 Independent Random Variables [168] 5.7 Jointly Gaussian Random Variables [174] 58 Joint Characteristic and Related Functions [178] 5.9 Transformations of Pairs of Random Variables [182] 5.9.1 Method 1, CDF Approach [187] 5.9.2 Method 2, Characteristic Function Approach [187] 5.9.3 Method 3, Conditional PDF Approach [187] 5.10 Complex Random Variables [193] 5.11 Engineering Application: Mutual Information, Channel Capacity, and Channel Coding [195] Exercises [200] MATLAB Exercises [205] 6 Multiple Random Variables [207] 6.1 Joint and Conditional PMFs, CDFs, and PDFs [207] 6.2 Expectations Involving Multiple Random Variables [209] 6.3 Gaussian Random Variables in Multiple Dimensions [211] 6.4 Transformations Involving Multiple Random Variables [215] 6.4.1 Linear Transformations [216] 6.4.2 Quadratic Transformations of Gaussian Random Vectors [221] 6.4.3 Order Statistics [223] 6.4.4 Coordinate Systems in Three Dimensions [225] 6.5 Engineering Application: Linear Prediction of Speech [227] Exercises [232] MATLAB Exercises [236] 7 Random Sequences and Series [239] 7.1 Independent and Identically Distributed Random Variables [239] 7.1.1 Estimating the Mean of IID Random Variables [240] 7.1.2 Estimating the Variance of IID Random Variables [245] 7.1.3 Estimating the CDF of IID Random Variables [247] 7.2 Convergence Modes of Random Sequences [249] 7.2.1 Convergence Everywhere [250] 7.2.2 Convergence Almost Everywhere [250] 7.2.3 Convergence in Probability [250] 7.2.4 Convergence in the Mean Square (MS) Sense [250] 7.2.5 Convergence in Distribution [250] 7.3 The Law of Large Numbers [251] 7.4 The Central Limit Theorem [253] 7.5 Confidence Intervals [258] 7.6 Random Sums of Random Variables [263] 7.7 Engineering Application: A Radar System [265] Exercises [271] MATLAB Exercises [275] 8 Random Processes [277] 8.1 Definition and Classification of Processes [277] 8.2 Mathematical Tools for Studying Random Processes [283] 8.3 Stationary and Ergodic Random Processes [291] 8.4 Properties of the Autocorrelation Function [300] 8.5 Gaussian Random Processes [301] 8.6 Poisson Processes [303] 8.7 Engineering Application: Shot Noise in a p-n Junction Diode [308] Exercises [313] MATLAB Exercises [319] 9 Markov Processes [323] 9.1 Definition and Examples of Markov Processes [323] 9.2 Calculating Transition and State Probabilities in Markov Chains [329] 9.3 Characterization of Markov Chains [335] 9.4 Continuous Time Markov Processes [342] 9.5 Engineering Application: A Computer Communications Network [354] 9.6 Engineering Application: A Telephone Exchange [357] Exercises [359] MATLAB Exercises [366] 10 Power Spectral Density [369] 10.1 Definition of Power Spectral Density [370] 10.2 TheWeiner-Khintchine-EinsteinTheorem [373] 10.3 Bandwidth of a Random Process [380] 10.4 Spectral Estimation [382] 10.4.1 Nonparametric Spectral Estimation [383] 10.4.2 Parametric Spectral Estimation [390] 10.5 Thermal Noise [394] 10.6 Engineering Application: PSDs of Digital Modulation Formats [397] Exercises [404] MATLAB Exercises [410] 11 Random Processes in Linear Systems [413] 11.1 Continuous Time Linear Systems [413] 11.2 Discrete Time Systems [418] 11.3 Noise Equivalent Bandwidth [419] 11.4 Signal-to-Noise Ratios [421] 11.5 The Matched Filter [423] 11.6 The Wiener Filter [427] 11.7 Bandlimited and Narrowband Random Processes [435] 11.8 Complex Envelopes [440] 11.9 Engineering Application: Noise in an Analog Communications System [442] Exercises [446] MATLAB Exercises [454] 12 Simulation Techniques [457] 12.1 Computer Generation of Random Variables [457] 12.1.1 Binary Pseudorandom Number Generators [458] 12.1.2 Non-Binary Pseudorandom Number Generators [461] 12.1.3 Generation of Random Numbers from a Specified Distribution [463] 12.1.4 Generation of Correlated Random Variables [465] 12.2 Generation of Random Processes [465] 12.2.1 Frequency Domain Approach [466] 12.2.2 Time Domain Approach [470] 12.2.3 Generation of Gaussian White Noise [475] 12.3 Simulation of Rare Events [476] 12.3.1 Monte Carlo Simulations [476] 12.3.2 Importance Sampling [479] 12.4 Engineering Application: Simulation of a Coded Digital Communication System [481] Exercises [483] MATLAB Exercises [486] Appendices [487] A Review of Set Theory [487] B Review of Linear Algebra [491] C Review of Signals and Systems [499] D Summary of Common Random Variables [505] E Mathematical Tables [517] F Numerical Methods for Evaluating the Q-Function [525] Index [531]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 60 M647 (Browse shelf) | Available | A-8493 |
Incluye índices.
1 Introduction [1] --
1.1 A Speech Recognition System [3] --
1.2 A Radar System [4] --
1.3 A Communication Network [5] --
2 Introduction to Probability Theory [7] --
2.1 Experiments, Sample Spaces, and Events [8] --
2.2 Axioms of Probability [11] --
2.3 Assigning Probabilities [14] --
2.4 Joint and Conditional Probabilities [18] --
2.5 Bayes's Theorem [22] --
2.6 Independence [25] --
2.7 Discrete Random Variables [28] --
2.7.1 Bernoulli Random Variable [31] --
2.7.2 Binomial Random Variable [32] --
2.7.3 Poisson Random Variable [33] --
2.7.4 Geometric Random Variable [34] --
2.8 Engineering Application: An Optical Communication System [35] --
Exercises [38] --
MATLAB Exercises [45] --
3 Random Variables, Distributions, and Density Functions [47] --
3.1 The Cumulative Distribution Function [48] --
3.2 The Probability Density Function [53] --
3.3 The Gaussian Random Variable [57] --
3.4 Other Important Random Variables [63] --
3.4.1 Uniform Random Variable [63] --
3.4.2 Exponential Random Variable [64] --
3.4.3 Laplace Random Variable [65] --
3.4.4 Gamma Random Variable [66] --
3.4.5 Erlang Random Variable [67] --
3.4.6 Chi-Squared Random Variable [67] --
3.4.7 Rayleigh Random Variable [68] --
3.4.8 Rician Random Variable [69] --
3.4.9 Cauchy Random Variable [69] --
3.5 Conditional Distribution and Density Functions [71] --
3.6 Engineering Application: Reliability and Failure Rates [77] --
Exercises [82] --
MATLAB Exercises [86] --
4 Operations on a Single Random Variable [87] --
4.1 Expected Value of a Random Variable [87] --
4.2 Expected Values of Functions of Random Variables [90] --
4.3 Moments [91] --
4.4 Central Moments [94] --
4.5 Conditional Expected Values [98] --
4.6 Transformations of Random Variables [100] --
4.7 Characteristic Functions [108] --
4.8 Probability Generating Functions [114] --
4.9 Moment Generating Functions [117] --
4.10 Evaluating Tail Probabilities [119] --
4.11 Engineering Application: Scalar Quantization [126] --
4.12 Engineering Application: Entropy and Source Coding [134] --
Exercises [138] --
MATLAB Exercises [145] --
5 Pairs of Random Variables [147] --
5.1 Joint Cumulative Distribution Functions [148] --
5.2 Joint Probability Density Functions [151] --
5.3 Joint Probability Mass Functions [157] --
5.4 Conditional Distribution, Density, and Mass Functions [159] --
5.5 Expected Values Involving Pairs of Random Variables [163] --
5.6 Independent Random Variables [168] --
5.7 Jointly Gaussian Random Variables [174] --
58 Joint Characteristic and Related Functions [178] --
5.9 Transformations of Pairs of Random Variables [182] --
5.9.1 Method 1, CDF Approach [187] --
5.9.2 Method 2, Characteristic Function Approach [187] --
5.9.3 Method 3, Conditional PDF Approach [187] --
5.10 Complex Random Variables [193] --
5.11 Engineering Application: Mutual Information, Channel Capacity, and Channel Coding [195] --
Exercises [200] --
MATLAB Exercises [205] --
6 Multiple Random Variables [207] --
6.1 Joint and Conditional PMFs, CDFs, and PDFs [207] --
6.2 Expectations Involving Multiple Random Variables [209] --
6.3 Gaussian Random Variables in Multiple Dimensions [211] --
6.4 Transformations Involving Multiple Random Variables [215] --
6.4.1 Linear Transformations [216] --
6.4.2 Quadratic Transformations of Gaussian Random Vectors [221] --
6.4.3 Order Statistics [223] --
6.4.4 Coordinate Systems in Three Dimensions [225] --
6.5 Engineering Application: Linear Prediction of Speech [227] --
Exercises [232] --
MATLAB Exercises [236] --
7 Random Sequences and Series [239] --
7.1 Independent and Identically Distributed Random Variables [239] --
7.1.1 Estimating the Mean of IID Random Variables [240] --
7.1.2 Estimating the Variance of IID Random Variables [245] --
7.1.3 Estimating the CDF of IID Random Variables [247] --
7.2 Convergence Modes of Random Sequences [249] --
7.2.1 Convergence Everywhere [250] --
7.2.2 Convergence Almost Everywhere [250] --
7.2.3 Convergence in Probability [250] --
7.2.4 Convergence in the Mean Square (MS) Sense [250] --
7.2.5 Convergence in Distribution [250] --
7.3 The Law of Large Numbers [251] --
7.4 The Central Limit Theorem [253] --
7.5 Confidence Intervals [258] --
7.6 Random Sums of Random Variables [263] --
7.7 Engineering Application: A Radar System [265] --
Exercises [271] --
MATLAB Exercises [275] --
8 Random Processes [277] --
8.1 Definition and Classification of Processes [277] --
8.2 Mathematical Tools for Studying Random Processes [283] --
8.3 Stationary and Ergodic Random Processes [291] --
8.4 Properties of the Autocorrelation Function [300] --
8.5 Gaussian Random Processes [301] --
8.6 Poisson Processes [303] --
8.7 Engineering Application: Shot Noise in a p-n Junction Diode [308] --
Exercises [313] --
MATLAB Exercises [319] --
9 Markov Processes [323] --
9.1 Definition and Examples of Markov Processes [323] --
9.2 Calculating Transition and State Probabilities in Markov Chains [329] --
9.3 Characterization of Markov Chains [335] --
9.4 Continuous Time Markov Processes [342] --
9.5 Engineering Application: A Computer Communications Network [354] --
9.6 Engineering Application: A Telephone Exchange [357] --
Exercises [359] --
MATLAB Exercises [366] --
10 Power Spectral Density [369] --
10.1 Definition of Power Spectral Density [370] --
10.2 TheWeiner-Khintchine-EinsteinTheorem [373] --
10.3 Bandwidth of a Random Process [380] --
10.4 Spectral Estimation [382] --
10.4.1 Nonparametric Spectral Estimation [383] --
10.4.2 Parametric Spectral Estimation [390] --
10.5 Thermal Noise [394] --
10.6 Engineering Application: PSDs of Digital Modulation Formats [397] --
Exercises [404] --
MATLAB Exercises [410] --
11 Random Processes in Linear Systems [413] --
11.1 Continuous Time Linear Systems [413] --
11.2 Discrete Time Systems [418] --
11.3 Noise Equivalent Bandwidth [419] --
11.4 Signal-to-Noise Ratios [421] --
11.5 The Matched Filter [423] --
11.6 The Wiener Filter [427] --
11.7 Bandlimited and Narrowband Random Processes [435] --
11.8 Complex Envelopes [440] --
11.9 Engineering Application: Noise in an Analog Communications System [442] --
Exercises [446] --
MATLAB Exercises [454] --
12 Simulation Techniques [457] --
12.1 Computer Generation of Random Variables [457] --
12.1.1 Binary Pseudorandom Number Generators [458] --
12.1.2 Non-Binary Pseudorandom Number Generators [461] --
12.1.3 Generation of Random Numbers from a Specified Distribution [463] --
12.1.4 Generation of Correlated Random Variables [465] --
12.2 Generation of Random Processes [465] --
12.2.1 Frequency Domain Approach [466] --
12.2.2 Time Domain Approach [470] --
12.2.3 Generation of Gaussian White Noise [475] --
12.3 Simulation of Rare Events [476] --
12.3.1 Monte Carlo Simulations [476] --
12.3.2 Importance Sampling [479] --
12.4 Engineering Application: Simulation of a Coded Digital Communication System [481] --
Exercises [483] --
MATLAB Exercises [486] --
Appendices [487] --
A Review of Set Theory [487] --
B Review of Linear Algebra [491] --
C Review of Signals and Systems [499] --
D Summary of Common Random Variables [505] --
E Mathematical Tables [517] --
F Numerical Methods for Evaluating the Q-Function [525] --
Index [531] --
MR, REVIEW #
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