Mikael Olofsson

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Signal Theory

Signal theory provides a mathematical toolbox for modeling and analysis of physical systems. Stochastic processes are used to model more or less unknown signals. Signal theory has applications in communication engineering, signal processing, automatic control, medical engineering, and more. This book starts off by reviewing the needed background from probability theory and signals & systems. Then stochastic processes are introduced, both in discrete and continuous time, together with the important tools auto-correlation function and power-spectral density. Separate chapters focus on analyzing linear filters, sampling & reconstruction, some nonlinearities and modulation in terms of stochastic processes. The modulation chapter includes noise analyses of the considered modulation methods assuming that thermal noise dominates the picture. A separate chapter briefly covers multi-dimensional signals and systems as a preparation for image processing. A chapter on spectral estimation is included, which could be used as a basis for computer-based laborations. Problems are given at the end of each chapter. Hints and answers to most of those problems are provided in appendices. The book is suitable for an advanced course on engineering aspects of stochastic processes. It is written with an electrical engineering student in mind, but should be useful in other engineering disciplines as well. We do not dwell on the innermost details of stochastic processes. Instead we focus on the ability to deal with stochastic processes in situations that could very well be models of real-world problems. This book provides tools and understanding that can be used as a preparation for in-depth studies of subjects such as communication engineering, image and signal processing or analysis, and automatic control, just to mention a few. This book is intended for engineering students with a background in probability theory on one hand and signals and systems on the other hand. No prior knowledge of stochastic processes is assumed. Tables and formulas for Signal Theory