Sampling Approximation And Signal Analysis

Author : Stephen D. Casey,M. Maurice Dodson,Paulo J. S. G. Ferreira,Ahmed Zayed
Publisher : Springer Nature
Page : 580 pages
File Size : 45,8 Mb
Release : 2024-01-04
Category : Mathematics
ISBN : 9783031411304

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Sampling, Approximation, and Signal Analysis by Stephen D. Casey,M. Maurice Dodson,Paulo J. S. G. Ferreira,Ahmed Zayed Pdf

During his long and distinguished career, J. Rowland Higgins (1935-2020) made a substantial impact on many mathematical fields through his work on sampling theory, his deep knowledge of its history, and his service to the community. This volume is a tribute to his work and legacy, featuring chapters written by distinguished mathematicians that explore cutting-edge research in sampling, approximation, signal analysis, and other related areas. An introductory chapter provides a biography of Higgins that explores his rich and unique life, along with a bibliography of his papers; a brief history of the SampTA meetings – of which he was a Founding Member – is also included. The remaining articles are grouped into four sections – classical sampling, theoretical extensions, frame theory, and applications of sampling theory – and explore Higgins’ contributions to these areas, as well as some of the latest developments.

Author : J. R. Higgins,R. L. Stens
Publisher : Oxford University Press
Page : 320 pages
File Size : 47,6 Mb
Release : 1999-11-25
Category : Mathematics
ISBN : 0198534965

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Sampling Theory in Fourier and Signal Analysis: Advanced Topics by J. R. Higgins,R. L. Stens Pdf

Volume 1 in this series laid the mathematical foundations of sampling theory; Volume 2 surveys the many applications of the theory both within mathematics and in other areas of science. Topics range over a wide variety of areas, and each application is given a modern treatment.

Author : John J. Benedetto,Paulo J.S.G. Ferreira
Publisher : Springer Science & Business Media
Page : 423 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201434

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Modern Sampling Theory by John J. Benedetto,Paulo J.S.G. Ferreira Pdf

A state-of-the-art edited survey covering all aspects of sampling theory. Theory, methods and applications are discussed in authoritative expositions ranging from multi-dimensional signal analysis to wavelet transforms. The book is an essential up-to-date resource.

Author : Robert J.II Marks
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461397571

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Advanced Topics in Shannon Sampling and Interpolation Theory by Robert J.II Marks Pdf

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 : Springer Science & Business Media
Page : 336 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461397083

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Introduction to Shannon Sampling and Interpolation Theory by Robert J. II Marks Pdf

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 : Ahmed I. Zayed,Gerhard Schmeisser
Publisher : Springer
Page : 487 pages
File Size : 52,8 Mb
Release : 2014-11-03
Category : Mathematics
ISBN : 9783319088013

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New Perspectives on Approximation and Sampling Theory by Ahmed I. Zayed,Gerhard Schmeisser Pdf

Paul Butzer, who is considered the academic father and grandfather of many prominent mathematicians, has established one of the best schools in approximation and sampling theory in the world. He is one of the leading figures in approximation, sampling theory, and harmonic analysis. Although on April 15, 2013, Paul Butzer turned 85 years old, remarkably, he is still an active research mathematician. In celebration of Paul Butzer’s 85th birthday, New Perspectives on Approximation and Sampling Theory is a collection of invited chapters on approximation, sampling, and harmonic analysis written by students, friends, colleagues, and prominent active mathematicians. Topics covered include approximation methods using wavelets, multi-scale analysis, frames, and special functions. New Perspectives on Approximation and Sampling Theory requires basic knowledge of mathematical analysis, but efforts were made to keep the exposition clear and the chapters self-contained. This volume will appeal to researchers and graduate students in mathematics, applied mathematics and engineering, in particular, engineers working in signal and image processing.

Author : Farokh Marvasti
Publisher : Springer Science & Business Media
Page : 938 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461512295

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Nonuniform Sampling by Farokh Marvasti Pdf

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 : John J. Benedetto,Ahmed I. Zayed
Publisher : Springer Science & Business Media
Page : 358 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817682125

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Sampling, Wavelets, and Tomography by John J. Benedetto,Ahmed I. Zayed Pdf

Sampling, wavelets, and tomography are three active areas of contemporary mathematics sharing common roots that lie at the heart of harmonic and Fourier analysis. The advent of new techniques in mathematical analysis has strengthened their interdependence and led to some new and interesting results in the field. This state-of-the-art book not only presents new results in these research areas, but it also demonstrates the role of sampling in both wavelet theory and tomography. Specific topics covered include: * Robustness of Regular Sampling in Sobolev Algebras * Irregular and Semi-Irregular Weyl-Heisenberg Frames * Adaptive Irregular Sampling in Meshfree Flow Simulation * Sampling Theorems for Non-Bandlimited Signals * Polynomial Matrix Factorization, Multidimensional Filter Banks, and Wavelets * Generalized Frame Multiresolution Analysis of Abstract Hilbert Spaces * Sampling Theory and Parallel-Beam Tomography * Thin-Plate Spline Interpolation in Medical Imaging * Filtered Back-Projection Algorithms for Spiral Cone Computed Tomography Aimed at mathematicians, scientists, and engineers working in signal and image processing and medical imaging, the work is designed to be accessible to an audience with diverse mathematical backgrounds. Although the volume reflects the contributions of renowned mathematicians and engineers, each chapter has an expository introduction written for the non-specialist. One of the key features of the book is an introductory chapter stressing the interdependence of the three main areas covered. A comprehensive index completes the work. Contributors: J.J. Benedetto, N.K. Bose, P.G. Casazza, Y.C. Eldar, H.G. Feichtinger, A. Faridani, A. Iske, S. Jaffard, A. Katsevich, S. Lertrattanapanich, G. Lauritsch, B. Mair, M. Papadakis, P.P. Vaidyanathan, T. Werther, D.C. Wilson, A.I. Zayed

Author : Yonina C. Eldar
Publisher : Cambridge University Press
Page : 837 pages
File Size : 43,8 Mb
Release : 2015-04-09
Category : Computers
ISBN : 9781107003392

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Sampling Theory by Yonina C. Eldar Pdf

A comprehensive guide to sampling for engineers, covering the fundamental mathematical underpinnings together with practical engineering principles and applications.

Author : Arie Feuer,Graham Goodwin
Publisher : Springer Science & Business Media
Page : 570 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461224600

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Sampling in Digital Signal Processing and Control by Arie Feuer,Graham Goodwin Pdf

Undoubtably one of the key factors influencing recent technology has been the advent of high speed computational tools. Virtually every advanced engi neering system we come in contact with these days depends upon some form of sampling and digital signal processing. Well known examples are digital tele phone systems, digital recording of audio signals and computer control. These developments have been matched by the appearance of a plethora of books which explain a variety of analysis, synthesis and design tools applica ble to sampled-data systems. The reader might therefore wonder what is distinc tive about the current book. Our observation of the existing literature is that the underlying continuous-time system is usually forgotten once the samples are tak en. The alternative point of view, adopted in this book, is to formulate the analy sis in such a way that the user is constantly reminded of the presence of the under lying continuous-time signals. We thus give emphasis to two aspects of sampled-data analysis: Firstly, we formulate the various algorithms so that the appropriate contin uous-time case is approached as the sampling rate increases. Secondly we place emphasis on the continuous-time output response rath er than simply focusing on the sampled response.

Author : Jeffrey A. Hogan,Joseph D. Lakey
Publisher : Springer Science & Business Media
Page : 258 pages
File Size : 48,9 Mb
Release : 2011-12-14
Category : Mathematics
ISBN : 9780817683078

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Duration and Bandwidth Limiting by Jeffrey A. Hogan,Joseph D. Lakey Pdf

Increasingly important in the field of communications, the study of time and band limiting is crucial for the modeling and analysis of multiband signals. This concise but comprehensive monograph is the first to be devoted specifically to this subdiscipline, providing a thorough investigation of its theory and applications. Through cutting-edge numerical methods, it develops the tools for applications not only to communications engineering, but also to optical engineering, geosciences, planetary sciences, and biomedicine. With broad coverage and a careful balance between rigor and readability, Duration and Bandwidth Limiting is a particularly original and valuable resource both for mathematicians interested in the field and for professional engineers with an interest in theory. While its main target audience is practicing scientists, the book may also serve as useful supplemental reading material for mathematically-based graduate courses in communications and signal processing.

Author : Xiaoping Shen,Ahmed I. Zayed
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 50,8 Mb
Release : 2012-09-18
Category : Technology & Engineering
ISBN : 9781461441441

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Multiscale Signal Analysis and Modeling by Xiaoping Shen,Ahmed I. Zayed Pdf

Multiscale Signal Analysis and Modeling presents recent advances in multiscale analysis and modeling using wavelets and other systems. This book also presents applications in digital signal processing using sampling theory and techniques from various function spaces, filter design, feature extraction and classification, signal and image representation/transmission, coding, nonparametric statistical signal processing, and statistical learning theory.

Author : Patrick Jungwirth
Publisher : Unknown
Page : 373 pages
File Size : 50,5 Mb
Release : 2018-02-08
Category : Electronic
ISBN : 1980218897

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Sampling Theory, and Analog-To-Digital Conversion (B/W Print Edition) by Patrick Jungwirth Pdf

**Note** This is a black and white print version (lower cost than other print version). another book on sampling theory and analog-to-digital conversion? This book takes a linear system theory approach to analog-to-digital conversion. From linear systems theory, we introduce sampling theory and use the tools from linear system theory to prove Shannon's sampling theorem. Shannon's sampling theorem shows how an analog signal can be converted to a discrete time signal and how the original can be exactly recovered from the discrete time signal. Digital is an approximation to discrete time so exact reconstruction is not possible; however, practically speaking the reconstructed signal is identical to the original analog signal. Digital is more than just 1's and 0's. Digital technology is universal. Once data is in digital form, it can be converted from one digital format to another without any additional loss of information (excluding lossy data compression). We use linear system theory and the sampling theorem to derive the model for an ideal analog to digital converter. We derive performance metrics from the ideal model. The performance metrics are put to good use to illustrate how to test and evaluate an analog-to-digital converter. Applications motivate the reader to apply concepts learned. More complex applications lead the reader to an introduction to software defined radios. Appendices provide summaries of the sampling theorem, communications engineering units, transform tables, and ADC model. Chapter 1 begins by introducing the digital world. Money is used to introduce analog, discrete, and digital. Chapter 2 starts off with a simple description of linear systems. Chapter 2 takes the reader from algebra, calculus, differential equations, Fourier transforms, and back to algebra. We want the reader to have a basic understanding of signal processing. Linear system theory provides the tools to prove the sampling theorem in Chapter 3. A graphical proof and analytical proof of the sampling theorem are presented in Chapter 4. We show why wagon wheels turn backwards in Western movies. Chapter 5 covers the binary math, we need to work with analog-to-digital converters. Code examples are provided for the "software interface" for an analog-to-digital converter. A useful part of Chapter 5 is how to solve the problem of a signed 10 bit analog-to-digital converter connected to a 16 bit microprocessor. The ideal analog-to-digital converter model is developed in Chapter 6. Chapter 7 introduces some common analog-to-digital converters: flash, pipeline, successive approximation register, and delta sigma (ΔΣ). Performance metrics and testing of analog-to-digital converters are found in Chapter 8. Chapter 9 presents sampling and analog-to-digital conversion applications. Chapter 10 covers a brief introduction to analog-to-digital converter datasheets focused on software defined radio applications. Chapter 11 presents an introduction to radio receiver block diagrams and finishes with a short introduction to software defined radios. Chapter 11 completes the journey from linear systems, to sampling theory, to analog-to-digital converters, and then the most useful part, applications. We hope this book serves as a good stepping stone to more complex applications. As computer power continues to increase and costs continue to drop, new applications will be found for the future. Be part of developing the future. If you have any suggestions for improvements, or find errors please email the book author (see book preface).

Author : Robert J II Marks
Publisher : Unknown
Page : 346 pages
File Size : 49,7 Mb
Release : 1990-11-06
Category : Electronic
ISBN : 146139709X

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Introduction to Shannon Sampling and Interpolation Theory by Robert J II Marks Pdf

Author : Willi Freeden,M. Zuhair Nashed
Publisher : CRC Press
Page : 184 pages
File Size : 52,6 Mb
Release : 2019-10-28
Category : Technology & Engineering
ISBN : 9781000757743

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Lattice Point Identities and Shannon-Type Sampling by Willi Freeden,M. Zuhair Nashed Pdf

Lattice Point Identities and Shannon-Type Sampling demonstrates that significant roots of many recent facets of Shannon's sampling theorem for multivariate signals rest on basic number-theoretic results. This book leads the reader through a research excursion, beginning from the Gaussian circle problem of the early nineteenth century, via the classical Hardy-Landau lattice point identity and the Hardy conjecture of the first half of the twentieth century, and the Shannon sampling theorem (its variants, generalizations and the fascinating stories about the cardinal series) of the second half of the twentieth century. The authors demonstrate how all these facets have resulted in new multivariate extensions of lattice point identities and Shannon-type sampling procedures of high practical applicability, thereby also providing a general reproducing kernel Hilbert space structure of an associated Paley-Wiener theory over (potato-like) bounded regions (cf. the cover illustration of the geoid), as well as the whole Euclidean space. All in all, the context of this book represents the fruits of cross-fertilization of various subjects, namely elliptic partial differential equations, Fourier inversion theory, constructive approximation involving Euler and Poisson summation formulas, inverse problems reflecting the multivariate antenna problem, and aspects of analytic and geometric number theory. Features: New convergence criteria for alternating series in multi-dimensional analysis Self-contained development of lattice point identities of analytic number theory Innovative lattice point approach to Shannon sampling theory Useful for students of multivariate constructive approximation, and indeed anyone interested in the applicability of signal processing to inverse problems.