Serpedin E., Chen T., Rajan D. (eds.) Mathematical Foundations for Signal Processing, Communications, and Networking

CRC Press, 2011. — 859 p.The rationale behind this textbook is to provide all the necessary mathematical background to facilitate the training and education of students and specialists working in the interrelated fields of signal processing, telecommunications, and networking. Our intention was to create a self-contained textbook that enables mastering both the fundamental results in the areas of signal processing, telecommunications and networking as well as the more advanced results and recent research trends in these areas.
In our collective academic experience, students often begin their graduate education with widely varying undergraduate backgrounds in terms of needed subjects such as probability theory, stochastic processes, statistics, linear algebra, calculus, optimization techniques, game theory, and queueing theory. While some students are well prepared for advanced courses in signal processing, telecommunications, and networking, others are not as well prepared and must make extra remedial efforts. However, obtaining the necessary mathematical background is often difficult because these topics are usually dispersed across a large number of courses, where the emphasis is frequently put on topics different than signal processing, telecommunications, and networking.
We hope that this textbook will serve as a reference for graduate-level students seeking to reach a common standard level of preparedness before undertaking more advanced specialized studies. We believe that this book will also be useful for researchers, engineers, and scientists working in related areas in electrical engineering, computer science, bioinformatics, and system biology. We also believe that this textbook could be used for a one-semester (or two-semester) graduate-level course that will help students acquire all the necessary mathematical background to pursue more advanced graduate courses. Both introductory and more advanced graduate-level courses could be taught based on this textbook. This textbook is accompanied by a Solutions Manual, and a set of viewgraphs will be made available to interested instructors. This textbook could also be used as a reference for self-teaching by a motivated professional who has graduate-level math skills.
Each chapter of this 20-chapter textbook was contributed by different experts in the areas of signal processing, telecommunications, and networking. Collectively, the chapters comprehensively cover a broad range of mathematical techniques that have been found to be necessary for a good understanding and mastering of the concepts and results from the fields of signal processing, telecommunications, and networking. Each chapter includes both mathematical theory as well as examples and homework exercises to illustrate the usage of the various mathematical concepts to solve different applications.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