Mathematical Foundations for Signal Processing, Communications, and Networking

Mathematical Foundations for Signal Processing, Communications, and Networking describes mathematical concepts and results important in the design, analysis, and optimization of signal processing algorithms, modern communication systems, and networks. Helping readers master key techniques and comprehend the current research literature, the book offers a comprehensive overview of methods and applications from linear algebra, numerical analysis, statistics, probability, stochastic processes, and optimization. From basic transforms to Monte Carlo simulation to linear programming, the text covers a broad range of mathematical techniques essential to understanding the concepts and results in signal processing, telecommunications, and networking. Along with discussing mathematical theory, each self-contained chapter presents examples that illustrate the use of various mathematical concepts to solve different applications. Each chapter also includes a set of homework exercises and readings for additional study. This text helps readers understand fundamental and advanced results as well as recent research trends in the interrelated fields of signal processing, telecommunications, and networking. It provides all the necessary mathematical background to prepare students for more advanced courses and train specialists working in these areas.

Erchin Serpedin is a professor in the Department of Electrical Engineering at Texas A&M University. Dr. Serpedin has been an associate editor of several journals and has received numerous honors, including a National Science Foundation CAREER Award, a National Research Council Fellow Award, and an American Society for Engineering Education Fellow Award. His research focuses on statistical signal processing, wireless communications, and bioinformatics. Thomas Chen is a professor of networks at Swansea University. Dr. Chen is technical editor for IEEE Press, editor-in-chief of IEEE Network, senior editor of IEEE Communications Magazine, and associate editor of International Journal of Security and Networks, Journal on Security and Communication Networks, and International Journal of Digital Crime and Forensics. His research areas encompass web filtering, web classification, traffic classification, smart grid security, privacy, cyber crime, and malware. Dinesh Rajan is an associate professor in the Department of Electrical Engineering at Southern Methodist University. An IEEE senior member, Dr. Rajan has received several awards, including a National Science Foundation CAREER Award. His research interests include communications theory, wireless networks, information theory, and computational imaging.

Introduction. Signal Processing Transforms. Linear Algebra. Elements of Galois Fields. Numerical Analysis. Combinatorics. Probability, Random Variables, and Stochastic Processes. Random Matrix Theory. Large Deviations. Fundamentals of Estimation Theory. Fundamentals of Detection Theory. Monte Carlo Methods for Statistical Signal Processing. Factor Graphs and Message Passing Algorithms. Unconstrained and Constrained Optimization Problems. Linear Programming and Mixed Integer Programming. Majorization Theory and Applications. Queueing Theory. Network Optimization Techniques. Game Theory. A Short Course on Frame Theory. Index.