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A signal theoretic introduction to random processes /
A fresh introduction to random processes utilizing signal theory By incorporating a signal theory basis, A Signal Theoretic Introduction to Random Processes presents a unique introduction to random processes with an emphasis on the important random phenomena encountered in the electronic and communi...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken, New Jersey :
John Wiley & Sons, Inc.,
[2015]
|
| Temas: | |
| Acceso en línea: | Texto completo (Requiere registro previo con correo institucional) |
MARC
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| 100 | 1 | |a Howard, Roy M. | |
| 245 | 1 | 2 | |a A signal theoretic introduction to random processes / |c Roy M. Howard. |
| 264 | 1 | |a Hoboken, New Jersey : |b John Wiley & Sons, Inc., |c [2015] | |
| 300 | |a 1 online resource | ||
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| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record and CIP data provided by publisher. | |
| 520 | |a A fresh introduction to random processes utilizing signal theory By incorporating a signal theory basis, A Signal Theoretic Introduction to Random Processes presents a unique introduction to random processes with an emphasis on the important random phenomena encountered in the electronic and communications engineering field. The strong mathematical and signal theory basis provides clarity and precision in the statement of results. The book also features: -A coherent account of the mathematical fundamentals and signal theory that underpin the presented material -Unique, in-depth coverage of material not typically found in introductory books -Emphasis on modeling and notation that facilitates development of random process theory -Coverage of the prototypical random phenomena encountered in electrical engineering -Detailed proofs of results -A related website with solutions to the problems found at the end of each chapter A Signal Theoretic Introduction to Random Processes is a useful textbook for upper-undergraduate and graduate-level courses in applied mathematics as well as electrical and communications engineering departments. The book is also an excellent reference for research engineers and scientists who need to characterize random phenomena in their research. | ||
| 505 | 0 | |a Title Page -- Copyright Page -- About the Author -- Contents -- Preface -- Chapter 1 A Signal Theoretic Introduction to Random Processes -- 1.1 INTRODUCTION -- 1.2 MOTIVATION -- 1.2.1 Usefulness of Randomness -- 1.2.2 Engineering -- 1.3 BOOK OVERVIEW -- Chapter 2 Background: Mathematics -- 2.1 INTRODUCTION -- 2.2 SET THEORY -- 2.2.1 Basic Definitions -- 2.2.2 Infinity -- 2.2.3 Supremum and Infimum -- 2.3 FUNCTION THEORY -- 2.3.1 Function Definition -- 2.3.2 Common Functions -- 2.3.3 Function Properties -- 2.4 MEASURE THEORY -- 2.4.1 Sigma Algebra -- 2.4.2 Measure -- 2.4.3 Lebesgue Measure -- 2.5 MEASURABLE FUNCTIONS -- 2.5.1 Simple or Elementary Functions -- 2.6 LEBESGUE INTEGRATION -- 2.6.1 The Lebesgue Integral -- 2.6.2 Demarcation of Signal Space -- 2.6.3 Miscellaneous Results -- 2.7 CONVERGENCE -- 2.7.1 Dominated and Monotone Convergence -- 2.8 LEBESGUE-STIELTJES MEASURE -- 2.8.1 Lebesgue-Stieltjes Measure: Monotonic Function Case -- 2.8.2 Lebesgue-Stieltjes Measure: Decreasing Function -- 2.8.3 Lebesgue-Stieltjes Measure: General Case -- 2.9 LEBESGUE-STIELTJES INTEGRATION -- 2.9.1 Motivation -- 2.9.2 Lebesgue-Stieltjes Integral -- 2.9.3 Lebesgue-Stieltjes Integrals: Specific Cases -- 2.10 MISCELLANEOUS RESULTS -- 2.11 PROBLEMS -- APPENDIX 2.A PROOF OF THEOREM 2.1 -- APPENDIX 2.B PROOF OF THEOREM 2.2 -- APPENDIX 2.C PROOF OF THEOREM 2.7 -- APPENDIX 2.D PROOF OF THEOREM 2.8 -- APPENDIX 2.E PROOF OF THEOREM 2.10 -- Chapter 3 Background: Signal Theory -- 3.1 INTRODUCTION -- 3.2 SIGNAL ORTHOGONALITY -- 3.2.1 Signal Decomposition -- 3.2.2 Generalization -- 3.2.3 Example: Hermite Basis Set -- 3.3 THEORY FOR DIRICHLET POINTS -- 3.3.1 Existence of Dirichlet Points -- 3.4 DIRAC DELTA -- 3.5 FOURIER THEORY -- 3.5.1 Fourier Series -- 3.5.2 Fourier Transform -- 3.5.3 Inverse Fourier Transform -- 3.5.4 Parsevalś Theorem -- 3.6 SIGNAL POWER. | |
| 505 | 8 | |a 3.6.1 Sinusoidal Basis Set -- 3.6.2 Arbitrary Basis Set -- 3.7 THE POWER SPECTRAL DENSITY -- 3.7.1 Energy Spectral Density -- 3.7.2 Power Spectral Density: Sinusoidal Basis Set -- 3.8 THE AUTOCORRELATION FUNCTION -- 3.8.1 Definition of the Autocorrelation Function -- 3.9 POWER SPECTRAL DENSITY-AUTOCORRELATION FUNCTION -- 3.9.1 Relationships for Alternative Autocorrelation Function -- 3.10 RESULTS FOR THE INFINITE INTERVAL -- 3.10.1 Average Power -- 3.10.2 The Power Spectral Density -- 3.10.3 Integrated Spectrum -- 3.10.4 Time Averaged Autocorrelation Function -- 3.10.5 Power Spectral Density-Autocorrelation Relationship -- 3.11 CONVERGENCE OF FOURIER COEFFICIENTS -- 3.11.1 Periodic Signal Case -- 3.11.2 Convergence of Fourier Coefficients to Zero -- 3.12 Cramerś Representation and Transform -- 3.12.1 Miscellaneous Mathematical Results -- 3.12.2 Cramer Representation and Transform -- 3.12.3 Initial Approach to the Cramer Transform -- 3.12.4 The Cramer Transform -- 3.12.5 Miscellaneous Results -- 3.12.6 Transform of Common Signals -- 3.12.7 Change in Transform -- 3.12.8 Linear Filtering -- 3.12.9 Integrated Spectrum, Spectrum, and Power Spectrum -- 3.12.10 Cramer Transform of Standard Signals -- 3.13 PROBLEMS -- APPENDIX 3.A PROOF OF THEOREM 3.5 -- APPENDIX 3.B PROOF OF THEOREM 3.8 -- APPENDIX 3.C FOURIER TRANSFORM AND PSD OF A SINUSOID -- APPENDIX 3.D PROOF OF THEOREM 3.14 -- APPENDIX 3.E PROOF OF THEOREM 3.19 -- APPENDIX 3.F PROOF OF THEOREM 3.23 -- APPENDIX 3.G PROOF OF THEOREM 3.24 -- APPENDIX 3.H PROOF OF THEOREM 3.25 -- APPENDIX 3.I PROOF OF THEOREM 3.26 -- APPENDIX 3.J CRAMER TRANSFORM OF UNIT STEP FUNCTION -- APPENDIX 3.K CRAMER TRANSFORM FOR SINUSOIDAL SIGNALS -- 3.K.1 Complex Exponential Case -- 3.K.2 Sine and Cosine on [−T,T] -- APPENDIX 3.L PROOF OF THEOREM 3.30 -- APPENDIX 3.M PROOF OF THEOREM 3.31 -- APPENDIX 3.N PROOF OF THEOREM 3.32. | |
| 505 | 8 | |a APPENDIX 3.O PROOF OF THEOREM 3.33 -- Chapter 4 Background: Probability and Random Variable Theory -- 4.1 INTRODUCTION -- 4.2 BASIC CONCEPTS: EXPERIMENTS-PROBABILITY THEORY -- 4.2.1 Experiments and Sample Spaces -- 4.2.2 Events -- 4.2.3 Probability of an Event -- 4.2.4 Conditional Probability -- 4.2.5 Independent Events -- 4.2.6 Countable and Uncountable Sample Spaces -- 4.3 THE RANDOM VARIABLE -- 4.3.1 Notes -- 4.3.2 Sample Spaces for Random Variables -- 4.3.3 Random Variable Based on Experimental Outcomes -- 4.4 DISCRETE AND CONTINUOUS RANDOM VARIABLES -- 4.4.1 Discrete Random Variables -- 4.4.2 Continuous Random Variables -- 4.4.3 Cumulative Distribution Function -- 4.5 STANDARD RANDOM VARIABLES -- 4.6 FUNCTIONS OF A RANDOM VARIABLE -- 4.7 EXPECTATION -- 4.7.1 Mean, Variance, and Moments of a Random Variable -- 4.7.2 Expectation of a Function of a Random Variable -- 4.7.3 Characteristic Function -- 4.8 GENERATION OF DATA CONSISTENT WITH DEFINED PDF -- 4.8.1 Example -- 4.9 VECTOR RANDOM VARIABLES -- 4.9.1 Random Variable Defined Based on Experimental Outcomes -- 4.9.2 Vector Random Variables -- 4.9.3 Sample Space for Vector Random Variable -- 4.10 PAIRS OF RANDOM VARIABLES -- 4.10.1 Notation -- 4.10.2 Joint Cumulative Distribution Function (Joint CDF) -- 4.10.3 Joint Probability Mass Function -- 4.10.4 Marginal Probability Mass Function -- 4.10.5 Joint Probability Density Function -- 4.10.6 Marginal Distribution and Density Functions -- 4.10.7 Linearity of Expectation Operator -- 4.10.8 Conditional Mass and Density Functions -- 4.11 COVARIANCE AND CORRELATION -- 4.11.1 Understanding Covariance -- 4.11.2 Uncorrelatedness -- 4.11.3 The Correlation Coefficient -- 4.12 SUMS OF RANDOM VARIABLES -- 4.12.1 Sum of Gaussian Random Variables -- 4.12.2 Difficulty in Determining the PDF of a Sum of Random Variables -- 4.13 JOINTLY GAUSSIAN RANDOM VARIABLES. | |
| 505 | 8 | |a 4.14 STIRLINGŚ FORMULA AND APPROXIMATIONS TO BINOMIAL -- 4.14.1 Binomial Probability Mass Function -- 4.14.2 Stirlingś Formula -- 4.14.3 DeMoivre-Laplace Theorem -- 4.14.4 Poisson Approximation to Binomial -- 4.15 PROBLEMS -- APPENDIX 4.A PROOF OF THEOREM 4.6 -- APPENDIX 4.B PROOF OF THEOREM 4.8 -- APPENDIX 4.C PROOF OF THEOREM 4.9 -- APPENDIX 4.D PROOF OF THEOREM 4.21 -- APPENDIX 4.E PROOF OF STIRLING'S FORMULA -- APPENDIX 4.F PROOF OF THEOREM 4.27 -- 4.F.1 Relative Error -- APPENDIX 4.G PROOF OF THEOREM 4.29 -- Chapter 5 Introduction to Random Processes -- 5.1 RANDOM PROCESSES -- 5.2 DEFINITION OF A RANDOM PROCESS -- 5.2.1 Notation -- 5.3 EXAMPLES OF RANDOM PROCESSES -- 5.3.1 On-Off Sinusoid -- 5.3.2 Sinusoid with Random Phase -- 5.3.3 Sinusoid with Random Amplitude -- 5.3.4 Amplitude and Frequency Modulation -- 5.3.5 Binary Digital Communication Signalling -- 5.4 EXPERIMENTS AND EXPERIMENTAL OUTCOMES -- 5.4.1 Experiments and Subexperiments -- 5.4.2 Specifying Sample Spaces: Single-Vector-Matrix Cases -- 5.5 PROTOTYPICAL EXPERIMENTS -- 5.5.1 Bernoulli Experiment -- 5.5.2 Poisson Experiment -- 5.5.3 Experiments with an Infinite Number of Subexperiments -- 5.6 RANDOM VARIABLES DEFINED BY A RANDOM PROCESS -- 5.7 CLASSIFICATION OF RANDOM PROCESSES -- 5.7.1 One-Dimensional Random Processes -- 5.7.2 Two-Dimensional Random Processes -- 5.7.3 Higher-Dimensional Random Processes -- 5.8 CLASSIFICATION: ONE-DIMENSIONAL RPs -- 5.8.1 Classification According to State -- 5.9 SUMS OF RANDOM PROCESSES -- 5.10 PROBLEMS -- Chapter 6 Prototypical Random Processes -- 6.1 INTRODUCTION -- 6.2 BERNOULLI RANDOM PROCESSES -- 6.2.1 Generalized Bernoulli Random Processes -- 6.2.2 Random Walk -- 6.3 POISSON RANDOM PROCESSES -- 6.3.1 Poisson Point Process -- 6.3.2 Poisson Counting Process -- 6.3.3 Shot Noise Random Process -- 6.3.4 Generalized Shot Noise. | |
| 505 | 8 | |a 6.3.5 Causal Random Telegraph Signal -- 6.3.6 Random Telegraph Signal: Type II -- 6.4 CLUSTERED RANDOM PROCESSES -- 6.4.1 Experiment for a Clustered Random Process -- 6.4.2 Clustered Point Random Process -- 6.4.3 Clustered Random Process -- 6.5 SIGNALLING RANDOM PROCESSES -- 6.5.1 Signalling Random Processes -- 6.5.2 Generalized Signalling Random Process -- 6.6 JITTER -- 6.6.1 Jittered Pulse Train -- 6.7 WHITE NOISE -- 6.7.1 White Noise: Approach I -- 6.7.2 White Noise: Approach II -- 6.7.3 Gaussian White Noise -- 6.7.4 Filtered White Noise -- 6.8 1/f NOISE -- 6.8.1 Model for 1/f Noise -- 6.8.2 Example -- 6.9 BIRTH-DEATH RANDOM PROCESSES -- 6.9.1 Experiment Underpinning Birth-Death Random Process -- 6.9.2 Birth-Death Random Processes -- 6.10 ORTHOGONAL INCREMENT RANDOM PROCESSES -- 6.10.1 Increment Function -- 6.10.2 Definition: Orthogonal Increment Random Process -- 6.10.3 Examples of Orthogonal Increment Random Processes -- 6.11 LINEAR FILTERING OF RANDOM PROCESSES -- 6.12 SUMMARY OF RANDOM PROCESSES -- 6.13 PROBLEMS -- APPENDIX 6.A PROOF OF THEOREM 6.4 -- Chapter 7 Characterizing Random Processes -- 7.1 INTRODUCTION -- 7.1.1 Notation for One-Dimensional Random Processes -- 7.1.2 Associated Random Processes -- 7.2 TIME EVOLUTION OF PMF OR PDF -- 7.3 FIRST-, SECOND-, AND HIGHER-ORDER CHARACTERIZATION -- 7.3.1 First-Order Characterization -- 7.3.2 Second-Order Characterization -- 7.3.3 Nth-Order Characterization -- 7.3.4 Mean and Variance and Average Power -- 7.3.5 Transient, Steady-State, Periodic, and Aperiodic Random Processes -- 7.4 AUTOCORRELATION AND POWER SPECTRAL DENSITY -- 7.4.1 Definitions for Individual Signals -- 7.4.2 Definitions for Autocorrelation and PSD -- 7.4.3 Simplified Notation: Countable Signal Sample Space Case -- 7.4.4 Notation: Vector Case -- 7.4.5 Infinite Interval Case -- 7.4.6 Existence: Finite Interval. | |
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| 650 | 0 | |a Stochastic processes. | |
| 650 | 0 | |a Random noise theory. | |
| 650 | 6 | |a Traitement du signal. | |
| 650 | 6 | |a Théorie du signal (Télécommunications) | |
| 650 | 6 | |a Processus stochastiques. | |
| 650 | 6 | |a Théorie du bruit aléatoire. | |
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| 650 | 7 | |a Signal processing. |2 fast |0 (OCoLC)fst01118281 | |
| 650 | 7 | |a Signal theory (Telecommunication) |2 fast |0 (OCoLC)fst01118306 | |
| 650 | 7 | |a Stochastic processes. |2 fast |0 (OCoLC)fst01133519 | |
| 653 | |a Australian | ||
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