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This book developed from a course given by the author to undergraduate and postgraduate students. It takes up Matrix Theory, Antenna Theory, and Probability Theory in detail. The first chapter on matrix theory discusses in reasonable depth the theory of Lie Algebras leading upto Cartan’s Classification Theory. It also discusses some basic elements of Functional Analysis and Operator Theory in infinite dimensional Banach and Hilbert spaces. The second chapter discusses Basic Probability Theory and the topics discussed find applications to Stochastic Filtering Theory for differential equations driven by white Gaussian noise. The third chapter is on Antenna Theory with a focus on Modern Quantum Antenna Theory. The book will be a valuable resource to students and early career researchers in the field of Mathametical Physics.
This book is a result of author's thirty-three years of experience in teaching and research in signal processing. The book will guide you from a review of continuous-time signals and systems, through the world of digital signal processing, up to some of the most advanced theory and techniques in adaptive systems, time-frequency analysis, and sparse signal processing. It provides simple examples and explanations for each, including the most complex transform, method, algorithm or approach presented in the book. The most sophisticated results in signal processing theory are illustrated on simple numerical examples. The book is written for students learning digital signal processing and for engineers and researchers refreshing their knowledge in this area. The selected topics are intended for advanced courses and for preparing the reader to solve problems in some of the state of art areas in signal processing. The book consists of three parts. After an introductory review part, the basic principles of digital signal processing are presented within Part two of the book. This part starts with Chapter two which deals with basic definitions, transforms, and properties of discrete-time signals. The sampling theorem, providing the essential relation between continuous-time and discrete-time signals, is presented in this chapter as well. Discrete Fourier transform and its applications to signal processing are the topic of the third chapter. Other common discrete transforms, like Cosine, Sine, Walsh-Hadamard, and Haar are also presented in this chapter. The z-transform, as a powerful tool for analysis of discrete-time systems, is the topic of Chapter four. Various methods for transforming a continuous-time system into a corresponding discrete-time system are derived and illustrated in Chapter five. Chapter six is dedicated to the forms of discrete-time system realizations. Basic definitions and properties of random discrete-time signals are given in Chapter six. Systems to process random discrete-time signals are considered in this chapter as well. Chapter six concludes with a short study of quantization effects. The presentation is supported by numerous illustrations and examples. Chapters within Part two are followed by a number of solved and unsolved problems for practice. The theory is explained in a simple way with a necessary mathematical rigor. The book provides simple examples and explanations for each presented transform, method, algorithm or approach. Sophisticated results in signal processing theory are illustrated by simple numerical examples. Part three of the book contains few selected topics in digital signal processing: adaptive discrete-time systems, time-frequency signal analysis, and processing of discrete-time sparse signals. This part could be studied within an advanced course in digital signal processing, following the basic course. Some parts from the selected topics may be included in tailoring a more extensive first course in digital signal processing as well. About the author: Ljubisa Stankovic is a professor at the University of Montenegro, IEEE Fellow for contributions to the Time-Frequency Signal Analysis, a member of the Montenegrin and European Academy of Sciences and Arts. He has been an Associate Editor of several world-leading journals in Signal Processing.
Offers a well-rounded, mathematical approach to problems in signal interpretation using the latest time, frequency, and mixed-domain methods Equally useful as a reference, an up-to-date review, a learning tool, and a resource for signal analysis techniques Provides a gradual introduction to the mathematics so that the less mathematically adept reader will not be overwhelmed with instant hard analysis Covers Hilbert spaces, complex analysis, distributions, random signals, analog Fourier transforms, and more
Being an inter-disciplinary subject, Signal Processing has application in almost all scientific fields. Applied Signal Processing tries to link between the analog and digital signal processing domains. Since the digital signal processing techniques have evolved from its analog counterpart, this book begins by explaining the fundamental concepts in analog signal processing and then progresses towards the digital signal processing. This will help the reader to gain a general overview of the whole subject and establish links between the various fundamental concepts. While the focus of this book is on the fundamentals of signal processing, the understanding of these topics greatly enhances the confident use as well as further development of the design and analysis of digital systems for various engineering and medical applications. Applied Signal Processing also prepares readers to further their knowledge in advanced topics within the field of signal processing.
This book is a collection of specific research problems in signal processing and their solutions. It touches upon most core topics, including active and passive processing, discrete-time and continuous signals, and design of filters and networks for specific applications. This unique collection of design problems and conceptual insights will be useful to graduate students, researchers, and professionals working on signal processing problems. In addition, the book can also be used as a supplementary text for graduate courses in advanced signal processing, and for professional development courses for practicing engineers.
Signal Processing for Neuroscientists introduces analysis techniques primarily aimed at neuroscientists and biomedical engineering students with a reasonable but modest background in mathematics, physics, and computer programming. The focus of this text is on what can be considered the 'golden trio' in the signal processing field: averaging, Fourier analysis, and filtering. Techniques such as convolution, correlation, coherence, and wavelet analysis are considered in the context of time and frequency domain analysis. The whole spectrum of signal analysis is covered, ranging from data acquisition to data processing; and from the mathematical background of the analysis to the practical application of processing algorithms. Overall, the approach to the mathematics is informal with a focus on basic understanding of the methods and their interrelationships rather than detailed proofs or derivations. One of the principle goals is to provide the reader with the background required to understand the principles of commercially available analyses software, and to allow him/her to construct his/her own analysis tools in an environment such as MATLAB®. - Multiple color illustrations are integrated in the text - Includes an introduction to biomedical signals, noise characteristics, and recording techniques - Basics and background for more advanced topics can be found in extensive notes and appendices - A Companion Website hosts the MATLAB scripts and several data files: http://www.elsevierdirect.com/companion.jsp?ISBN=9780123708670
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This second volume, edited and authored by world leading experts, gives a review of the principles, methods and techniques of important and emerging research topics and technologies in communications and radar engineering. With this reference source you will: - Quickly grasp a new area of research - Understand the underlying principles of a topic and its application - Ascertain how a topic relates to other areas and learn of the research issues yet to be resolved - Quick tutorial reviews of important and emerging topics of research in array and statistical signal processing - Presents core principles and shows their application - Reference content on core principles, technologies, algorithms and applications - Comprehensive references to journal articles and other literature on which to build further, more specific and detailed knowledge - Edited by leading people in the field who, through their reputation, have been able to commission experts to write on a particular topic