Much of that which is ordinal is modeled as analog. Most computational engines on the other hand are dig- ital. Transforming from analog to digital is straightforward: we simply sample. Regaining the original signal from these samples or assessing the information lost in the sampling process are the fundamental questions addressed by sampling and interpolation theory. This book deals with understanding, generalizing, and extending the cardinal series of Shannon sampling theory. The fundamental form of this series states, remarkably, that a bandlimited signal is uniquely specified by its sufficiently close equally spaced samples. The contents of this book evolved from a set of lecture notes prepared for a graduate survey course on Shannon sampling and interpolation theory. The course was taught at the Department of Electrical Engineering at the University of Washington, Seattle. Each of the seven chapters in this book includes a list of references specific to that chapter. A sequel to this book will contain an extensive bibliography on the subject. The author has also opted to include solutions to selected exercises in the Appendix.

Advanced Topics in Shannon Sampling and Interpolation Theory is the second volume of a textbook on signal analysis solely devoted to the topic of sampling and restoration of continuous time signals and images. Sampling and reconstruction are fundamental problems in any field that deals with real-time signals or images, including communication engineering, image processing, seismology, speech recognition, and digital signal processing. This second volume includes contributions from leading researchers in the field on such topics as Gabor's signal expansion, sampling in optical image formation, linear prediction theory, polar and spiral sampling theory, interpolation from nonuniform samples, an extension of Papoulis's generalized sampling expansion to higher dimensions, and applications of sampling theory to optics and to time-frequency representations. The exhaustive bibliography on Shannon sampling theory will make this an invaluable research tool as well as an excellent text for students planning further research in the field.

Advances in Shannon's Sampling Theory provides an up-to-date discussion of sampling theory, emphasizing the interaction between sampling theory and other branches of mathematical analysis, including the theory of boundary-value problems, frames, wavelets, multiresolution analysis, special functions, and functional analysis. The author not only traces the history and development of the theory, but also presents original research and results that have never before appeared in book form. Recent techniques covered include the Feichtinger-Gröchenig sampling theory; frames, wavelets, multiresolution analysis and sampling; boundary-value problems and sampling theorems; and special functions and sampling theorems. The book will interest graduate students and professionals in electrical engineering, communications, and applied mathematics.

The chapters of this volume are based on talks given at the eleventh international Sampling Theory and Applications conference held in 2015 at American University in Washington, D.C. The papers highlight state-of-the-art advances and trends in sampling theory and related areas of application, such as signal and image processing. Chapters have been written by prominent mathematicians, applied scientists, and engineers with an expertise in sampling theory. Claude Shannon’s 100th birthday is also celebrated, including an introductory essay that highlights Shannon’s profound influence on the field. The topics covered include both theory and applications, such as: • Compressed sensing• Non-uniform and wave sampling• A-to-D conversion• Finite rate of innovation• Time-frequency analysis• Operator theory• Mobile sampling issues Sampling: Theory and Applications is ideal for mathematicians, engineers, and applied scientists working in sampling theory or related areas.

Our understanding of nature is often through nonuniform observations in space or time. In space, one normally observes the important features of an object, such as edges. The less important features are interpolated. History is a collection of important events that are nonuniformly spaced in time. Historians infer between events (interpolation) and politicians and stock market analysts forecast the future from past and present events (extrapolation). The 20 chapters of Nonuniform Sampling: Theory and Practice contain contributions by leading researchers in nonuniform and Shannon sampling, zero crossing, and interpolation theory. Its practical applications include NMR, seismology, speech and image coding, modulation and coding, optimal content, array processing, and digital filter design. It has a tutorial outlook for practising engineers and advanced students in science, engineering, and mathematics. It is also a useful reference for scientists and engineers working in the areas of medical imaging, geophysics, astronomy, biomedical engineering, computer graphics, digital filter design, speech and video processing, and phased array radar.

Sampling theory is that branch of mathematics that seeks to reconstruct functions from its values at a discrete set of points. The fundamental result in sampling theory known as "Shannon's sampling theorem" has many applications to signal processing and communications engineering. I demonstrate Shannon's result via complex interpolation methods. I then quote a result that uses these methods to solve interpolation problems on unions of noncommensurate lattices, which are created via a specific number of the- oretic guidelines. These interpolations give Shannon-type reconstructions on these lattices. I close by doing simulations in MATLAB of the sampling reconstructions on these noncommensurate grids.

Essential background reading for engineers and scientists working in such fields as communications, control, signal, and image processing, radar and sonar, radio astronomy, seismology, remote sensing, and instrumentation. The book can be used as a textbook for a single course, as well as a combination of an introductory and an advanced course, or even for two separate courses, one in signal detection, the other in estimation.

In two editions spanning more than a decade, The Electrical Engineering Handbook stands as the definitive reference to the multidisciplinary field of electrical engineering. Our knowledge continues to grow, and so does the Handbook. For the third edition, it has grown into a set of six books carefully focused on specialized areas or fields of study. Each one represents a concise yet definitive collection of key concepts, models, and equations in its respective domain, thoughtfully gathered for convenient access. Combined, they constitute the most comprehensive, authoritative resource available. Circuits, Signals, and Speech and Image Processing presents all of the basic information related to electric circuits and components, analysis of circuits, the use of the Laplace transform, as well as signal, speech, and image processing using filters and algorithms. It also examines emerging areas such as text to speech synthesis, real-time processing, and embedded signal processing. Electronics, Power Electronics, Optoelectronics, Microwaves, Electromagnetics, and Radar delves into the fields of electronics, integrated circuits, power electronics, optoelectronics, electromagnetics, light waves, and radar, supplying all of the basic information required for a deep understanding of each area. It also devotes a section to electrical effects and devices and explores the emerging fields of microlithography and power electronics. Sensors, Nanoscience, Biomedical Engineering, and Instruments provides thorough coverage of sensors, materials and nanoscience, instruments and measurements, and biomedical systems and devices, including all of the basic information required to thoroughly understand each area. It explores the emerging fields of sensors, nanotechnologies, and biological effects. Broadcasting and Optical Communication Technology explores communications, information theory, and devices, covering all of the basic information needed for a thorough understanding of these areas. It also examines the emerging areas of adaptive estimation and optical communication. Computers, Software Engineering, and Digital Devices examines digital and logical devices, displays, testing, software, and computers, presenting the fundamental concepts needed to ensure a thorough understanding of each field. It treats the emerging fields of programmable logic, hardware description languages, and parallel computing in detail. Systems, Controls, Embedded Systems, Energy, and Machines explores in detail the fields of energy devices, machines, and systems as well as control systems. It provides all of the fundamental concepts needed for thorough, in-depth understanding of each area and devotes special attention to the emerging area of embedded systems. Encompassing the work of the world's foremost experts in their respective specialties, The Electrical Engineering Handbook, Third Edition remains the most convenient, reliable source of information available. This edition features the latest developments, the broadest scope of coverage, and new material on nanotechnologies, fuel cells, embedded systems, and biometrics. The engineering community has relied on the Handbook for more than twelve years, and it will continue to be a platform to launch the next wave of advancements. The Handbook's latest incarnation features a protective slipcase, which helps you stay organized without overwhelming your bookshelf. It is an attractive addition to any collection, and will help keep each volume of the Handbook as fresh as your latest research.