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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 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. 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 Coef...
