Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Ito calculus, the central theorems in the field, and such approximation schemes as stochastic Runge-Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-driven derivations and computational assignments. MATLAB/Octave source code is available for download, promoting hands-on work with the methods.

Random Signals, Noise and Filtering develops the theory of random processes and its application to the study of systems and analysis of random data. The text covers three important areas: (1) fundamentals and examples of random process models, (2) applications of probabilistic models: signal detection, and filtering, and (3) statistical estimation--measurement and analysis of random data to determine the structure and parameter values of probabilistic models. This volume by Breipohl and Shanmugan offers the only one-volume treatment of the fundamentals of random process models, their applications, and data analysis.

This unique introduction to the foundational concepts of cyber-physical systems (CPS) describes key design principles and emerging research trends in detail. Several interdisciplinary applications are covered, with a focus on the wide-area management of infrastructures including electric power systems, air transportation networks, and health care systems. Design, control and optimization of cyber-physical infrastructures are discussed, addressing security and privacy issues of networked CPS, presenting graph-theoretic and numerical approaches to CPS evaluation and monitoring, and providing readers with the knowledge needed to operate CPS in a reliable, efficient, and secure manner. Exercises are included. This is an ideal resource for researchers and graduate students in electrical engineering and computer science, as well as for practitioners using cyber-physical systems in aerospace and automotive engineering, medical technology, and large-scale infrastructure operations.

Signals and Images: Advances and Results in Speech, Estimation, Compression, Recognition, Filtering, and Processing cohesively combines contributions from field experts to deliver a comprehensive account of the latest developments in signal processing. These experts detail the results of their research related to audio and speech enhancement, acoustic image estimation, video compression, biometric recognition, hyperspectral image analysis, tensor decomposition with applications in communications, adaptive sparse-interpolated filtering, signal processing for power line communications, bio-inspired signal processing, seismic data processing, arithmetic transforms for spectrum computation, particle filtering in cooperative networks, three-dimensional television, and more. This book not only shows how signal processing theory is applied in current and emerging technologies, but also demonstrates how to tackle key problems such as how to enhance speech in the time domain, improve audio quality, and meet the desired electrical consumption target for controlling carbon emissions. Signals and Images: Advances and Results in Speech, Estimation, Compression, Recognition, Filtering, and Processing serves as a guide to the next generation of signal processing solutions for speech and video coding, hearing aid devices, big data processing, smartphones, smart digital communications, acoustic sensors, and beyond.

Nowadays, many aspects of electrical and electronic engineering are essentially applications of DSP. This is due to the focus on processing information in the form of digital signals, using certain DSP hardware designed to execute software. Fundamental topics in digital signal processing are introduced with theory, analytical tables, and applications with simulation tools. The book provides a collection of solved problems on digital signal processing and statistical signal processing. The solutions are based directly on the math-formulas given in extensive tables throughout the book, so the reader can solve practical problems on signal processing quickly and efficiently. FEATURES Explains how applications of DSP can be implemented in certain programming environments designed for real time systems, ex. biomedical signal analysis and medical image processing. Pairs theory with basic concepts and supporting analytical tables. Includes an extensive collection of solved problems throughout the text. Fosters the ability to solve practical problems on signal processing without focusing on extended theory. Covers the modeling process and addresses broader fundamental issues.

Understand the fundamentals of wireless and MIMO communication with this accessible and comprehensive text. Viewing the subject through an information theory lens, but also drawing on other perspectives, it provides a sound treatment of the key concepts underpinning contemporary wireless communication and MIMO, all the way to massive MIMO. Authoritative and insightful, it includes over 330 worked examples and 450 homework problems, with solutions and MATLAB code and data available online. Altogether, this is an excellent resource for instructors and graduate students, as well as an outstanding reference for researchers and practicing engineers.

Written specifically for biomedical engineers, Biosignal and Medical Image Processing, Third Edition provides a complete set of signal and image processing tools, including diagnostic decision-making tools, and classification methods. Thoroughly revised and updated, it supplies important new material on nonlinear methods for describing and classifying signals, including entropy-based methods and scaling methods. A full set of PowerPoint slides covering the material in each chapter and problem solutions is available to instructors for download. See What's New in the Third Edition: Two new chapters on nonlinear methods for describing and classifying signals. Additional examples with biological data such as EEG, ECG, respiration and heart rate variability Nearly double the number of end-of-chapter problems MATLAB (R) incorporated throughout the text Data "cleaning" methods commonly used in such areas as heart rate variability studies The text provides a general understanding of image processing sufficient to allow intelligent application of the concepts, including a description of the underlying mathematical principals when needed. Throughout this textbook, signal and image processing concepts are implemented using the MATLAB (R) software package and several of its toolboxes. The challenge of covering a broad range of topics at a useful, working depth is motivated by current trends in biomedical engineering education, particularly at the graduate level where a comprehensive education must be attained with a minimum number of courses. This has led to the development of "core" courses to be taken by all students. This text was written for just such a core course. It is also suitable for an upper-level undergraduate course and would also be of value for students in other disciplines that would benefit from a working knowledge of signal and image processing.

Designed to cover the fundamental concepts of digital signal processing, the book introduces topics such as discrete-time signals, the z-transform, frequency analysis, discrete and fast Fourier transforms, digital filters, FIR, statistical DSP, applications, and more. DSP has been applied in most disciplines ranging from engineering to telecommunications, and from astronomy to medical imaging. This book focuses on the fundamentals of DSP, namely on the representation of signals by mathematical models and on the processing of signals by discrete-time systems. Features Designed to cover the fundamental concepts of DSP Introduces topics such as discrete-time signals, the z-transform, frequency analysis, discrete and fast Fourier transforms, digital filters, FIR, statistical DSP, applications, and more Features a variety of exercises and a glossary

Discover a modern approach to the analysis, modeling and design of high sensitivity phased arrays. Network theory, numerical methods and computational electromagnetic simulation techniques are uniquely combined to enable full system analysis and design optimization. Beamforming and array signal processing theory are integrated into the treatment from the start. Digital signal processing methods such as polyphase filtering and RFI mitigation are described, along with technologies for real-time hardware implementation. Key concepts from interferometric imaging used in radio telescopes are also considered. A basic development of theory and modeling techniques is accompanied by problem sets that guide readers in developing modeling codes that retain the simplicity of the classical array factor method while incorporating mutual coupling effects and interactions between elements. Combining current research trends with pedagogical material suitable for a first-year graduate course, this is an invaluable resource for students, teachers, researchers, and practicing RF/microwave and antenna design engineers.

This self-contained, systematic treatment of multivariate approximation begins with classical linear approximation, and moves on to contemporary nonlinear approximation. It covers substantial new developments in the linear approximation theory of classes with mixed smoothness, and shows how it is directly related to deep problems in other areas of mathematics. For example, numerical integration of these classes is closely related to discrepancy theory and to nonlinear approximation with respect to special redundant dictionaries, and estimates of the entropy numbers of classes with mixed smoothness are closely related to (in some cases equivalent to) the Small Ball Problem from probability theory. The useful background material included in the book makes it accessible to graduate students. Researchers will find that the many open problems in the theory outlined in the book provide helpful directions and guidance for their own research in this exciting and active area.

"An excellent introductory book" (Review of the First Edition in the International Journal of Electrical Engineering Education) "…it will serve as a reference book in this area for a long time" (Review of Revised Edition in Zentralblatt für Mathematik (Germany))

Firmly established over the last decade as the essential introductory Digital Signal Processing (DSP) text, this second edition reflects the growing importance of random digital signals and random DSP in the undergraduate syllabus by including two new chapters. The authors’ practical, problem-solving approach to DSP continues in this new material, which is packed up by additional worked examples and computer programs. The book now features:

• fundamentals of digital signals and systems
• time and frequency domain analysis and processing, including digital convolution and the Discrete and Fast Fourier Transforms
• design and practical application of digital filters
• description and processing of random signals, including correlation, filtering, and the detection of signals in noise

In many areas of human endeavor, the systems involved are not available for direct measurement. Instead, by combining mathematical models for a system's evolution with partial observations of its evolving state, we can make reasonable inferences about it. The increasing complexity of the modern world makes this analysis and synthesis of high-volume data an essential feature in many real-world problems.
The celebrated Kalman-Bucy filter, designed for linear dynamical systems with linearly structured measurements, is the most famous Bayesian filter. Its generalizations to nonlinear systems and/or observations are collectively referred to as nonlinear filtering (NLF), an extension of the Bayesian framework to the estimation, prediction, and interpolation of nonlinear stochastic dynamics. NLF uses a stochastic model to make inferences about an evolving system and is a theoretically optimal algorithm.
The breadth of its applications, firmly established and still emerging, is simply astounding. Early uses such as cryptography, tracking, and guidance were mostly of a military nature. Since then, the scope has exploded. It includes the study of global climate, estimating the state of the economy, identifying tumors using non-invasive methods, and much more.
The Oxford Handbook of Nonlinear Filtering is the first comprehensive written resource for the subject. It contains classical and recent results and applications, with contributions from 58 authors. Collated into 10 parts, it covers the foundations of nonlinear filtering, connections to stochastic partial differential equations, stability and asymptotic analysis, estimation and control, approximation theory and numerical methods for solving the nonlinear filtering problem (including particle methods). It also contains a part dedicated to the application of nonlinear filtering to several problems in mathematical finance.

Written in the intuitive yet rigorous style that readers of A Foundation in Digital Communication have come to expect, this second edition includes entirely new chapters on the radar problem (with Lyapunov's theorem) and intersymbol interference channels, new discussion of the baseband representation of passband noise, and a simpler, more geometric derivation of the optimal receiver for the additive white Gaussian noise channel. Other key topics covered include the definition of the power spectral density of nonstationary stochastic processes, the geometry of the space of energy-limited signals, the isometry properties of the Fourier transform, and complex sampling. Including over 500 homework problems and all the necessary mathematical background, this is the ideal text for one- or two-semester graduate courses on digital communications and courses on stochastic processes and detection theory. Solutions to problems and video lectures are available online.

This book demonstrates the optimal adversarial attacks against several important signal processing algorithms. Through presenting the optimal attacks in wireless sensor networks, array signal processing, principal component analysis, etc, the authors reveal the robustness of the signal processing algorithms against adversarial attacks. Since data quality is crucial in signal processing, the adversary that can poison the data will be a significant threat to signal processing. Therefore, it is necessary and urgent to investigate the behavior of machine learning algorithms in signal processing under adversarial attacks. The authors in this book mainly examine the adversarial robustness of three commonly used machine learning algorithms in signal processing respectively: linear regression, LASSO-based feature selection, and principal component analysis (PCA). As to linear regression, the authors derive the optimal poisoning data sample and the optimal feature modifications, and also demonstrate the effectiveness of the attack against a wireless distributed learning system. The authors further extend the linear regression to LASSO-based feature selection and study the best strategy to mislead the learning system to select the wrong features. The authors find the optimal attack strategy by solving a bi-level optimization problem and also illustrate how this attack influences array signal processing and weather data analysis. In the end, the authors consider the adversarial robustness of the subspace learning problem. The authors examine the optimal modification strategy under the energy constraints to delude the PCA-based subspace learning algorithm. This book targets researchers working in machine learning, electronic information, and information theory as well as advanced-level students studying these subjects. R&D engineers who are working in machine learning, adversarial machine learning, robust machine learning, and technical consultants working on the security and robustness of machine learning are likely to purchase this book as a reference guide.

Accurate, robust and fast image reconstruction is a critical task in many scientific, industrial and medical applications. Over the last decade, image reconstruction has been revolutionized by the rise of compressive imaging. It has fundamentally changed the way modern image reconstruction is performed. This in-depth treatment of the subject commences with a practical introduction to compressive imaging, supplemented with examples and downloadable code, intended for readers without extensive background in the subject. Next, it introduces core topics in compressive imaging - including compressed sensing, wavelets and optimization - in a concise yet rigorous way, before providing a detailed treatment of the mathematics of compressive imaging. The final part is devoted to recent trends in compressive imaging: deep learning and neural networks. With an eye to the next decade of imaging research, and using both empirical and mathematical insights, it examines the potential benefits and the pitfalls of these latest approaches.

Now available in a three-volume set, this updated and expanded edition of the bestselling The Digital Signal Processing Handbook continues to provide the engineering community with authoritative coverage of the fundamental and specialized aspects of information-bearing signals in digital form. Encompassing essential background material, technical details, standards, and software, the second edition reflects cutting-edge information on signal processing algorithms and protocols related to speech, audio, multimedia, and video processing technology associated with standards ranging from WiMax to MP3 audio, low-power/high-performance DSPs, color image processing, and chips on video. Drawing on the experience of leading engineers, researchers, and scholars, the three-volume set contains 29 new chapters that address multimedia and Internet technologies, tomography, radar systems, architecture, standards, and future applications in speech, acoustics, video, radar, and telecommunications. Emphasizing theoretical concepts, Digital Signal Processing Fundamentals provides comprehensive coverage of the basic foundations of DSP and includes the following parts: Signals and Systems; Signal Representation and Quantization; Fourier Transforms; Digital Filtering; Statistical Signal Processing; Adaptive Filtering; Inverse Problems and Signal Reconstruction; and Time-Frequency and Multirate Signal Processing.

Digital Signal Processing:A Primer with MATLAB (R) provides excellent coverage of discrete-time signals and systems. At the beginning of each chapter, an abstract states the chapter objectives. All principles are also presented in a lucid, logical, step-by-step approach. As much as possible, the authors avoid wordiness and detail overload that could hide concepts and impede understanding. In recognition of requirements by the Accreditation Board for Engineering and Technology (ABET) on integrating computer tools, the use of MATLAB (R) is encouraged in a student-friendly manner. MATLAB is introduced in Appendix C and applied gradually throughout the book. Each illustrative example is immediately followed by practice problems along with its answer. Students can follow the example step-by-step to solve the practice problems without flipping pages or looking at the end of the book for answers. These practice problems test students' comprehension and reinforce key concepts before moving onto the next section. Toward the end of each chapter, the authors discuss some application aspects of the concepts covered in the chapter. The material covered in the chapter is applied to at least one or two practical problems. It helps students see how the concepts are used in real-life situations. Also, thoroughly worked examples are given liberally at the end of every section. These examples give students a solid grasp of the solutions as well as the confidence to solve similar problems themselves. Some of hte problems are solved in two or three ways to facilitate a deeper understanding and comparison of different approaches. Designed for a three-hour semester course, Digital Signal Processing:A Primer with MATLAB (R) is intended as a textbook for a senior-level undergraduate student in electrical and computer engineering. The prerequisites for a course based on this book are knowledge of standard mathematics, including calculus and complex numbers.

This comprehensive and engaging textbook introduces the basic principles and techniques of signal processing, from the fundamental ideas of signals and systems theory to real-world applications. Students are introduced to the powerful foundations of modern signal processing, including the basic geometry of Hilbert space, the mathematics of Fourier transforms, and essentials of sampling, interpolation, approximation and compression The authors discuss real-world issues and hurdles to using these tools, and ways of adapting them to overcome problems of finiteness and localization, the limitations of uncertainty, and computational costs. It includes over 160 homework problems and over 220 worked examples, specifically designed to test and expand students' understanding of the fundamentals of signal processing, and is accompanied by extensive online materials designed to aid learning, including Mathematica (R) resources and interactive demonstrations.

Machine Learning: A Bayesian and Optimization Perspective, 2nd edition, gives a unified perspective on machine learning by covering both pillars of supervised learning, namely regression and classification. The book starts with the basics, including mean square, least squares and maximum likelihood methods, ridge regression, Bayesian decision theory classification, logistic regression, and decision trees. It then progresses to more recent techniques, covering sparse modelling methods, learning in reproducing kernel Hilbert spaces and support vector machines, Bayesian inference with a focus on the EM algorithm and its approximate inference variational versions, Monte Carlo methods, probabilistic graphical models focusing on Bayesian networks, hidden Markov models and particle filtering. Dimensionality reduction and latent variables modelling are also considered in depth. This palette of techniques concludes with an extended chapter on neural networks and deep learning architectures. The book also covers the fundamentals of statistical parameter estimation, Wiener and Kalman filtering, convexity and convex optimization, including a chapter on stochastic approximation and the gradient descent family of algorithms, presenting related online learning techniques as well as concepts and algorithmic versions for distributed optimization. Focusing on the physical reasoning behind the mathematics, without sacrificing rigor, all the various methods and techniques are explained in depth, supported by examples and problems, giving an invaluable resource to the student and researcher for understanding and applying machine learning concepts. Most of the chapters include typical case studies and computer exercises, both in MATLAB and Python. The chapters are written to be as self-contained as possible, making the text suitable for different courses: pattern recognition, statistical/adaptive signal processing, statistical/Bayesian learning, as well as courses on sparse modeling, deep learning, and probabilistic graphical models. New to this edition: Complete re-write of the chapter on Neural Networks and Deep Learning to reflect the latest advances since the 1st edition. The chapter, starting from the basic perceptron and feed-forward neural networks concepts, now presents an in depth treatment of deep networks, including recent optimization algorithms, batch normalization, regularization techniques such as the dropout method, convolutional neural networks, recurrent neural networks, attention mechanisms, adversarial examples and training, capsule networks and generative architectures, such as restricted Boltzman machines (RBMs), variational autoencoders and generative adversarial networks (GANs). Expanded treatment of Bayesian learning to include nonparametric Bayesian methods, with a focus on the Chinese restaurant and the Indian buffet processes.

Stream processing is a novel distributed computing paradigm that supports the gathering, processing, and analysis of high-volume, heterogeneous, continuous data streams, to extract insights and actionable results in real time. This comprehensive, hands-on guide combining the fundamental building blocks and emerging research in stream processing is ideal for application designers, system builders, analytic developers, as well as students and researchers in the field. This book introduces the key components of the stream computing paradigm, including the distributed system infrastructure, the programming model, design patterns, and streaming analytics. The explanation of the underlying theoretical principles, illustrative examples and implementations using the IBM InfoSphere Streams SPL language, and real-world case studies provide students and practitioners with a comprehensive understanding of such applications and the middleware that supports them.

Starting with essential maths, fundamentals of signals and systems, and classical concepts of DSP, this book presents, from an application-oriented perspective, modern concepts and methods of DSP including machine learning for audio acoustics and engineering. Content highlights include but are not limited to room acoustic parameter measurements, filter design, codecs, machine learning for audio pattern recognition and machine audition, spatial audio, array technologies and hearing aids. Some research outcomes are fed into book as worked examples. As a research informed text, the book attempts to present DSP and machine learning from a new and more relevant angle to acousticians and audio engineers. Some MATLAB (R) codes or frameworks of algorithms are given as downloads available on the CRC Press website. Suggested exploration and mini project ideas are given for "proof of concept" type of exercises and directions for further study and investigation. The book is intended for researchers, professionals, and senior year students in the field of audio acoustics.

Provides a modern mathematical approach to the design of communication networks for graduate students, blending control, optimization, and stochastic network theories. A broad range of performance analysis tools are discussed, including important advanced topics that have been made accessible to students for the first time. Taking a top-down approach to network protocol design, the authors begin with the deterministic model and progress to more sophisticated models. Network algorithms and protocols are tied closely to the theory, illustrating the practical engineering applications of each topic. The background behind the mathematical analyses is given before the formal proofs and is supported by worked examples, enabling students to understand the big picture before going into the detailed theory. End-of-chapter problems cover a range of difficulties, with complex problems broken into several parts, and hints to many problems are provided to guide students. Full solutions are available online for instructors.

Seismic data must be interpreted using digital signal processing techniques in order to create accurate representations of petroleum reservoirs and the interior structure of the Earth. This book provides an advanced overview of digital signal processing (DSP) and its applications to exploration seismology using real-world examples. The book begins by introducing seismic theory, describing how to identify seismic events in terms of signals and noise, and how to convert seismic data into the language of DSP. Deterministic DSP is then covered, together with non-conventional sampling techniques. The final part covers statistical seismic signal processing via Wiener optimum filtering, deconvolution, linear-prediction filtering and seismic wavelet processing. With over sixty end-of-chapter exercises, seismic data sets and data processing MATLAB codes included, this is an ideal resource for electrical engineering students unfamiliar with seismic data, and for Earth Scientists and petroleum professionals interested in DSP techniques.

This book is a companion to the original book by Johnson and Graham, High-Speed Digital Design: A Handbook of Black Magic, Prentice-Hall, 1993. The two books may be used separately, or together. They cover different material. KEY TOPICS: High-Speed Signal Propagation delves into the issues relevant to signal transmission at the upper limits of speed and distance. This book shows you how to transmit faster and further than ever before, considering today's digital networks and wireless devices. You'll find it packed with practical advice, including material never before published on the subject of high-speed design. Johnson also presents a complete and unified theory of signal propagation for all metallic media from cables to pcb traces to chips. It includes numerous examples, pictures, tables, and wide-ranging discussion of the high-speed properties of transmission lines. This is not yet another book on the subject of ringing and crosstalk. It's about long, high-speed channels operating at the upper limits of speed and distance. EDN Magazine will feature and 1- 1/2 page excerpt from Johnson's book each month, for seven months leading up to the book's publication. MARKET: The reader should know what a transmission line is, and have some general understanding of the relationship between the time domain and the frequency domain. Digital logic designers, system architects, EMC specialists, technicians, and printed wiring layout professionals. Anyone who works with long, high-speed signal channels fighting tradeoffs between speed and distance.

A selection of papers presented at the four-yearly IMA conference on Mathematics in Signal Processing. Covering a wide range of recent topics, including excellent review papers and original research.