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Informationen zum Autor Roy M. Howard, PhD , is Adjunct Senior Research Fellow in the Department of Electrical and Computer Engineering at Curtin University, Perth, Australia. His research expertise includes modeling of stochastic processes, signal theory, and low noise amplifier design. Klappentext A fresh introduction to random processes utilizing signal theoryBy 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 chapterA 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. Zusammenfassung Presenting a rigorous introduction to the modelling and characterization of random phenomena, this book stands out from the existing texts in this field by characterizing random processes in signal theory. Inhaltsverzeichnis Preface xiii 1 A Signal Theoretic Introduction to Random Processes 1 1.1 Introduction 1 1.2 Motivation 2 1.3 Book Overview 8 2 Background: Mathematics 11 2.1 Introduction 11 2.2 Set Theory 11 2.3 Function Theory 13 2.4 Measure Theory 18 2.5 Measurable Functions 24 2.6 Lebesgue Integration 28 2.7 Convergence 37 2.8 Lebesgue-Stieltjes Measure 39 2.9 Lebesgue-Stieltjes Integration 50 2.10 Miscellaneous Results 61 2.11 Problems 62 3 Background: Signal Theory 71 3.1 Introduction 71 3.2 Signal Orthogonality 71 3.3 Theory for Dirichlet Points 75 3.4 Dirac Delta 78 3.5 Fourier Theory 79 3.6 Signal Power 82 3.7 The Power Spectral Density 84 3.8 The Autocorrelation Function 91 3.9 Power Spectral Density-Autocorrelation Function 95 3.10 Results for the Infinite Interval 96 3.11 Convergence of Fourier Coefficients 103 3.12 Cramer's Representation and Transform 106 3.13 Problems 125 4 Background: Probability and Random Variable Theory 153 4.1 Introduction 153 4.2 Basic Concepts: Experiments-Probability Theory 153 4.3 The Random Variable 160 4.4 Discrete and Continuous Random Variables 162 4.5 Standard Random Variables 165 4.6 Functions of a Random Variable 165 4.7 Expectation 166 4.8 Generation of Data Consistent with Defined PDF 172 4.9 Vector Random Variables 173 4.10 Pairs of Random Variables 175 4.11 Covariance and Correlation 186 4.12 Sums of Random Variables 191 4.13 Jointly Gaussian Random Variables 193 4.14 Stirling's Formula and Approximations to Binomial 194 4.15 Problems 199 5 Introduction to Random Processes 219 5.1 Random Processes 219 5.2 Definition of a Random Process 219 5.3 Examples of Random Processes 221 5.4 Experiments and Experimental Outcomes 225 5.5 Prototypical Experimen...
