Holdings: Probability and random processes

Probability and random processes: with applications to signal processing and communications

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Bibliographic Details
Main Authors:	Miller, Scott L. (Author), Childers, Donald G. (Author)
Format:	Book
Language:	English
Published:	Amsterdam [u.a.] Elsevier Academic Press 2012
Edition:	2. ed.
Subjects:	Mathematik Signal processing > Mathematics Probabilities Stochastic processes Wahrscheinlichkeitstheorie Sprachverarbeitung Stochastischer Prozess
Online Access:	Inhaltsverzeichnis
Item Description:	Includes bibliographical references and index
Physical Description:	xii, 611 p. ill. 25 cm
ISBN:	9780123869814 0123869811

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MARC


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adam_text	Contents Preface ..............................................................................................................xi Chapter 1: Introduction ......................................................................................1 1.1 A Speech Recognition System .............................................................................2 1.2 A Radar System ....................................................................................................4 1.3 A Communication Network ..................................................................................4 Chapter 2: Introduction to Probability Theory .......................................................7 2.1 Experiments, Sample Spaces, and Events ............................................................7 2.2 Axioms of Probability .........................................................................................10 2.3 Assigning Probabilities ........................................................................................13 2.4 Joint and Conditional Probabilities .....................................................................17 2.5 Basic Combinatorics ............................................................................................20 2.6 Bayes s Theorem .................................................................................................27 2.7 Independence .......................................................................................................29 2.8 Discrete Random Variables .................................................................................32 2.9 Engineering Application — An Optical Communication System .........................38 Exercises ..............................................................................................................43 MATLAB Exercises ............................................................................................61 Chapter 3: Random Variables, Distributions, and Density Functions .....................63 3.1 The Cumulative Distribution Function ................................................................64 3.2 The Probability Density Function ........................................................................69 3.3 The Gaussian Random Variable ..........................................................................71 3.4 Other Important Random Variables ....................................................................78 3.4.1 Uniform Random Variable .............................................................................78 3.4.2 Exponential Random Variable ...........,..........................................................79 3.4.3 Laplace Random Variable .............................................................................80 3.4.4 Gamma Random Variable ..........................................................,..................81 3.4.5 Erlang Random Variable ............................................................................... 81 3.4.6 Chi-Squamd Random Variable .....................................................................82 3.4.7 Rayleigh Random Variable ...........................................................................82 3.4.8 Ridan Random Variable ...............................................................................83 3.4.9 Cauchy Random Variable .............................................................................84 vi Contents 3.5 Conditional Distribution and Density Functions ................................................85 3.6 Engineering Application: Reliability and Failure Rates .....................................91 Exercises .............................................................................................................97 MATLAB Exercises .......................................................................................... Ю9 Chapter 4: Operations on a Single Random Variable ..........................................111 4.1 Expected Value of a Random Variable ............................................................. HI 4.2 Expected Values of Functions of Random Variables .......................................113 4.3 Moments ...........................................................................................................115 4.4 Central Moments ...............................................................................................117 4.5 Conditional Expected Values ............................................................................121 4.6 Transformations of Random Variables .............................................................122 4.6. і Monotonically Increasing Functions ...........................................................122 4.6.2 Monotonically Decreasing Functions ..........................................................124 4.6.3 Nonmonotonic Functions ............................................................................125 4.7 Characteristic Functions ...................................................................................130 4.8 Probability-Generating Functions .....................................................................136 4.9 Moment-Generating Functions .........................................................................139 4.10 Evaluating Tail Probabilities ..........................................................................140 4.11 Engineering Application — Scalar Quantization .............................................148 4.12 Engineering Application — Entropy and Source Coding ................................155 Exercises .........................................................................................................159 MATLAB Exercises ........................................................................................174 Chapter 5; Pairs of Random Variables .............................................................. 177 5.1 Joint Cumulative Distribution Functions ..........................................................178 5.2 Joint Probability Density Functions ................................,.................................180 5.3 Joint Probability Mass Functions ........................................................,.............186 5.4 Conditional Distribution, Density, and Mass Functions ...................................188 5.5 Expected Values Involving Pairs of Random Variables ...................................192 5.6 Independent Random Variables ........................................................................197 5.7 Jointly Gaussian Random Variables .................................................................202 5.8 Joint Characteristic and Related Functions .......................................................206 5.9 Transformations of Pairs of Random Variables ...............................................210 5.10 Complex Random Variables ...........................................................................219 5.11 Engineering Application: Mutual Mormation, Channel Capacity, and Channel Coding .......................................................................221 Exercises .........................................................................................................227 MATLAB Exercises .......................................................„............................... 242 Otapter6: Multiple Random Variables ____.....___...............................«...........245 6.1 Joint and Conditional PMFs, CDFs, and PDFs ..................................,.............245 6.2 Expectations Involving Multiple Random Variables ...............................,........247 6.3 Gaussian Random Variables in Multiple Dimensions ......................................249 6.4 Transformatioßs Involving Multiple Random Variables ..................................252 Contents vìi 6.4.1 Linear Transformations ................................................................................253 6.4.2 Quadratic Transformations of Gaussian Random Vectors .........................257 6.4.3 Order Statistics ............................................................................................260 6.4.4 Coordinate Systems in Three Dimensions ..................................................262 6.5 Estimation and Detection ...................................................................................264 6.5.1 Maximum a Posteriori Estimation ..............................................................265 6.5.2 Maximum Likelihood Estimation ...............................................................267 6.5.3 Minimum Mean Square Error Estimation ...................................................268 6.6 Engineering Application: Linear Prediction of Speech .....................................272 Exercises ............................................................................................................277 MATLAB Exercises ...........................................................................................287 Chapter 7: Random Sums and Sequences ..........................................................289 7.1 Independent and Identically Distributed Random Variables .............................289 7.1.1 Estimating the Mean of IID Random Variables ..........................................290 7.1.2 Estimating the Variance of IID Random Variables ....................................295 7.1.3 Estimating the CDF of IID Random Variables ...........................................297 7.2 Convergence Modes of Random Sequences .....................................................298 7.2.1 Convergence Everywhere ...........................................................................300 7.2.2 Convergence Almost Every where ..............................................................301 7.2.3 Convergence in Probability .........................................................................301 7.2.4 Convergence is the Mean Square Sense ......................................................302 7.2.5 Convergence in Distribution .......................................................................302 7.3 The Law of Large Numbers ...............................................................................304 7.4 The Central Limit Theorem ...............................................................................306 7.5 Confidence Intervals ..........................................................................................310 7.6 Random Sums of Random Variables .................................................................315 7.7 Engineering Application: A Radar System .......................................................317 Exercises ............................................................................................................325 MATLAB Exercises ...........................................................................................334 ChapterS: Random Processes ..........................................................................335 8.1 Definition and Classification of Processes ........................................................335 8.2 Mathematical Tools for Studying Random Processes .......................................340 8.3 Stationary and Ergodic Random Processes .......................................................348 8.4 Properties of the Autocorrelation Function .......................................................356 8.5 Gaussian Random Processes .............................................................................357 8.6 Poisson Processes ..............................................................................................360 8.7 Engineering Application — Shot Noise in ар -η Junction Diode .......................365 Exercises ............................................................................................................371 MATLAB Exercises ...........................................................................................381 Chapter 9: Markov Processes .......................................................................... 383 9.1 Definition and Examples of Markov Processes .................................................383 9.2 Calculating Transition and State Probabilities in Markov Chains ....................388 9.3 Characterizatioa of Markov Chains ..................................................................,394 9.4 Continuous Time Markov Processes ...........................................,.....................401 9.5 Engineering Application: A Computer Communication Network ....................413 viii Contents 9.6 Engineering Application: A Telephone Exchange ...........................................416 Exercises ...........................................................................................................419 MATLAB Exercises.......................................................................................... 427 Chapter 10: Power Spectral Density .................................................................429 10.1 Definition of PSD ...........................................................................................430 10.2 The Wiener-Khintchine-Einstein Theorem ...................................................433 10.3 Bandwidth of a Random Process ....................................................................439 10.4 Spectral Estimation .........................................................................................441 10.4.1 Non-parametric Spectral Estimation .........................................................441 10.4.2 Parametric Spectral Estimation .................................................................448 10.5 Thermal Noise .................................................................................................452 10.6 Engineering Application: PSDs of Digital Modulation Formats ....................455 Exercises .........................................................................................................463 MATLAB Exercises ........................................................................................469 Chapter 11: Random Processes in Linear Systems ..............................................473 11.1 Continuous Time Linear Systems ...................................................................473 11.2 Discrete-Time Linear Systems ........................................................................477 11.3 Noise Equivalent Bandwidth ..........................................................................479 11.4 Signal-to-Noise Ratios ....................................................................................480 11.5 The Matched Filter ..........................................................................................482 11.6 The Wiener Filter ............................................................................................486 11.7 Bandlimited and Narrowband Random Processes ..........................................494 11.8 Complex Envelopes ........................................................................................499 11.9 Engineering Application: An Analog Communication System ......................500 Exercises .........................................................................................................505 MATLAB Exercises ........................................................................................514 Chapter 12: Simulation Techniques ..................................................................517 12.1 Computer Generation of Random Variables ..................................................517 12.1.1 Binary Pseudorandom Number Generators ...............................................517 12.1.2 Nonbinary Pseudorandom Number Generators .........................................521 12.1.3 Generation of Random Numbers from a Specified Distribution ...............523 12.1.4 Generation of Correlated Random Variables ............................................524 12.2 Generation of Random Processes ...................................................................525 12.2.1 Frequency Domain Approach ....................................................................525 12.2.2 Time Domain Approach ............................................................................529 12.2.3 Generation of Gaussian White Noise ........................................................533 12.3 Simulation of Rare Events ..............................................................................534 12.3.1 Monte Carlo Simulations ..............................................,............................535 12.3.2 Importance Sampling .................................................................................537 12.4 Engineering Application: Simulation of a Coded Digital Communication System ........,.........................................................................539 Exercises .......................................................,..............„.......................,„.......543 MATLAB Exercises ...........................,............................................................546 Contents ix Appendices A Review of Set Theory ...........................................................................................547 В Review of Linear Algebra .....................................................................................551 С Review of Signals and Systems ...........................................................................559 D Summary of Common Random Variables ...........................................................565 E Mathematical Tables ............................................................................................577 F Numerical Methods for Evaluating the Q-Function .............................................587 Index .............................................................................................................593
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spelling	Miller, Scott L. Verfasser aut Probability and random processes with applications to signal processing and communications Scott L. Miller, Donald Childers 2. ed. Amsterdam [u.a.] Elsevier Academic Press 2012 xii, 611 p. ill. 25 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematik Signal processing Mathematics Probabilities Stochastic processes Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Sprachverarbeitung (DE-588)4116579-2 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Sprachverarbeitung (DE-588)4116579-2 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Childers, Donald G. Verfasser aut Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025338565&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Miller, Scott L. Childers, Donald G. Probability and random processes with applications to signal processing and communications Mathematik Signal processing Mathematics Probabilities Stochastic processes Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Sprachverarbeitung (DE-588)4116579-2 gnd Stochastischer Prozess (DE-588)4057630-9 gnd
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title	Probability and random processes with applications to signal processing and communications
title_auth	Probability and random processes with applications to signal processing and communications
title_exact_search	Probability and random processes with applications to signal processing and communications
title_full	Probability and random processes with applications to signal processing and communications Scott L. Miller, Donald Childers
title_fullStr	Probability and random processes with applications to signal processing and communications Scott L. Miller, Donald Childers
title_full_unstemmed	Probability and random processes with applications to signal processing and communications Scott L. Miller, Donald Childers
title_short	Probability and random processes
title_sort	probability and random processes with applications to signal processing and communications
title_sub	with applications to signal processing and communications
topic	Mathematik Signal processing Mathematics Probabilities Stochastic processes Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Sprachverarbeitung (DE-588)4116579-2 gnd Stochastischer Prozess (DE-588)4057630-9 gnd
topic_facet	Mathematik Signal processing Mathematics Probabilities Stochastic processes Wahrscheinlichkeitstheorie Sprachverarbeitung Stochastischer Prozess
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