Author: Jennifer K. Smith
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 112

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Book Description

Author: Kristian Seip
Publisher: American Mathematical Soc.
ISBN: 0821835548
Category : Mathematics
Languages : en
Pages : 153

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Book Description
Based on a series of six lectures given by the author at the University of Michigan, this book is intended as an introduction to the topic of interpolation and sampling in analytic function spaces. The three major topics covered are Nevanlinna-Pick interpolation, Carleson's interpolation theorem, an

Author: Robert J. II Marks
Publisher: Springer Science & Business Media
ISBN: 1461397081
Category : Technology & Engineering
Languages : en
Pages : 336

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Book Description
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.

Author: Jonathan Richard Partington
Publisher: Oxford University Press
ISBN: 9780198500247
Category : Language Arts & Disciplines
Languages : en
Pages : 286

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Book Description
With this text, Jonathan Partington explores the application of mathematical analysis to problems of interpolation and engineering, including systems identification, and signal processing and sampling.

Author: Robert J.II Marks
Publisher: Springer Science & Business Media
ISBN: 146139757X
Category : Technology & Engineering
Languages : en
Pages : 364

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Book Description
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.

Author: Robert J II Marks
Publisher:
ISBN: 9781461397090
Category :
Languages : en
Pages : 346

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Book Description

Author: Alexander M. Olevskii
Publisher: American Mathematical Soc.
ISBN: 147042889X
Category : Mathematics
Languages : en
Pages : 152

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Book Description
The classical sampling problem is to reconstruct entire functions with given spectrum S from their values on a discrete set L. From the geometric point of view, the possibility of such reconstruction is equivalent to determining for which sets L the exponential system with frequencies in L forms a frame in the space L2(S). The book also treats the problem of interpolation of discrete functions by analytic ones with spectrum in S and the problem of completeness of discrete translates. The size and arithmetic structure of both the spectrum S and the discrete set L play a crucial role in these problems. After an elementary introduction, the authors give a new presentation of classical results due to Beurling, Kahane, and Landau. The main part of the book focuses on recent progress in the area, such as construction of universal sampling sets, high-dimensional and non-analytic phenomena. The reader will see how methods of harmonic and complex analysis interplay with various important concepts in different areas, such as Minkowski's lattice, Kolmogorov's width, and Meyer's quasicrystals. The book is addressed to graduate students and researchers interested in analysis and its applications. Due to its many exercises, mostly given with hints, the book could be useful for undergraduates.

Author: Farokh Marvasti
Publisher: Springer Science & Business Media
ISBN: 1461512298
Category : Technology & Engineering
Languages : en
Pages : 938

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Book Description
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.

Author: A. J. Lee
Publisher:
ISBN:
Category : Interpolation
Languages : en
Pages : 40

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Book Description

Author: Martin Schetzen
Publisher:
ISBN:
Category :
Languages : en
Pages : 73

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Book Description
A study of linear interpolation of sampled random processes is presented in this report. A mathematical model of a sampler and of an interpolator are first developed. These models are used to derive general expressions for the mean-square interpolation error. The specific examples of zero- and first-order interpolation are used to illustrate the expressions. The problem of optimum interpolation is then formulated using the criterion that the mean-square error be a minimum. Explicit expressions for the optimum causal linear filter for interpolation using corrupted samples and expressions for the resulting minimum mean-square error are obtained. These results are illustrated by some specific examples of practical importance. A simple upper bound of the mean-square error is derived and a generalization of the sampling theorem for random functions is obtained by use of this bound. Although the important case of periodic sampling is emphasized in this report, the extension to a periodic sampling is given. (Author).