Random Processes in Linear Systems

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9780130673916: Random Processes in Linear Systems
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This book provides an introduction to random processes, and includes content in digital communications and signal processing. Chapter topics cover Probability and Random Variables—Review and Notation, an introduction to Random Processes, Linear Filtering of Random Processes, and Frequency-Domain Analysis of Random Processes in Linear Systems. For practicing engineers.

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This book provides an introduction to random processes that is suitable for advanced undergraduates, beginning graduate students, and practicing engineers. Portions of the book have been used as a text for 12 to 15 hours of instruction in the second part of an undergraduate course in probability and random processes at the University of Illinois. The material was taught by the author and other faculty members to juniors and seniors majoring in electrical engineering or computer engineering. The course emphasized Chapters 2 and 3, but it included parts of Chapter 4. For thorough coverage of Chapter 4, more time is required. The manuscript for the book has also served as the text for the first few weeks of several graduate courses in communications at a number of universities. In most of these courses, Chapters 2-4 are covered completely. In additi6n, the manuscript has been used by many beginning graduate students who needed to acquire a solid understanding of second-order random processes in preparation for graduate courses in digital communications, wireless communication systems, or signal processing. Typically, such a student's undergraduate education included basic probability and linear systems, but not random processes.

The book presents a very brief review of probability, but this material is intended primarily to introduce the notation for subsequent chapters. The student is expected to have a good understanding of probability and random variables from a previous course on probability or from the earlier portion of a course on probability and random processes. An adequate understanding of the concepts needed for the student to begin a study of random processes typically requires approximately 25 to 30 hours of instruction based on a text such as A First Course in Probability by Sheldon Ross or Introduction to Probability and Its Applications by Richard Scheaffer. Such instruction might be given in the first part of a course for which this book serves as a text for the second part.

There is enough material here for a separate one-quarter course in random processes at the undergraduate or beginning graduate level. For a graduate course it is anticipated that the instructor may wish to expand upon the applications in Section 3.6. If time permits, the instructor may choose to require the students to complete a project, perhaps along the lines of one of the applications in that section. The book could also serve as a supplemental text for a one- or two-semester course in digital communications or signal processing.

This book is designed for self-study by engineers and beginning graduate students, and the manuscript has been used in that way by many readers over the past several years. The basic tools of linear system analysis are reviewed and integrated into the exposition of second-order random processes. The discussions are sufficiently detailed to walk the reader through the applications of the concepts and techniques that are presented. Several examples and exercises with solutions are provided to test the reader's understanding along the way. Each chapter has a set of problems that further test the reader's understanding and extend some of the topics presented in the text.

I wish to thank each of the instructors who taught from the manuscript for the book and supplied suggestions and corrections. Special thanks are due Professor Dilip Sarwate of the University of Illinois, Professor James Lehnert of Purdue University, and Professors John Komo and Daniel Noneaker of Clemson University. Each was kind enough to teach from one or more versions of the manuscript and provide extensive feedback that improved the book. Finally, I wish to express my appreciation to the students who suffered through numerous revisions of the manuscript and furnished lists of corrections.

MICHAEL B. PURSLEY

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