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 addresses both the basic mathematical concepts employed in the areas of signal processing, telecommunications and networking as well as the more advanced mathematical results associated with the recent research trends in these areas. This textbook describes mathematical concepts and results that are important in the design, analysis, and optimization of signal processing algorithms, modern communication systems, and networks. It offers a comprehensive overview of methods and applications from linear algebra, numerical analysis, statistics, probability, stochastic processes, and optimization. This textbook consists of twenty self-contained chapters and includes examples, homework problems, and references in each chapter. A Solution Manual and a set of viewgraphs are available for the interested instructors.
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 queuing theory. While some students are well prepared for advanced courses in signal processing, telecommunications and networking, others are not as well prepared and must take many preparatory courses. 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 that have little relevance to signal processing, telecommunications and networking. Therefore, we wanted to create a textbook where all the important mathematical results and concepts with large applicability in signal processing, communications and networking are presented in a concise manner so that a student can build the required mathematical background in a short time interval by taking one or two graduate level courses based on this textbook.
We hope that this textbook will serve as a reference for graduate level students to reach a common standard level of preparedness before undertaking more advanced specialized studies. We believe that this book will be also 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 has already been tested in several universities in courses such as Foundations for Signal Processing and Communications, to prepare the students with the necessary mathematical background before taking graduate level courses in signal processing, telecommunications and networking. This textbook is accompanied by a Solution Manual and a set of viewgraphs. The instructors interested in obtaining these materials
should contact Dr. Erchin Serpedin (email: serpedin@ece.tamu.edu).
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