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Modern Sampling Theory

Mathematics and Applications

  • Book
  • © 2001

Overview

Editors:
  1. John J. Benedetto

    1. Department of Mathematics, University of Maryland, College Park, USA

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  2. Paulo J. S. G. Ferreira

    1. Departamento de Electronica e Telecommunicacoes, Universidade de Aveiro, Aveiro, Portugal

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Introduction

    1. Introduction

      • John J. Benedetto, Paulo J. S. G. Ferreira
      Pages 1-26

  3. On the Transmission Capacity of the “Ether” and Wire in Electrocommunications

    1. On the Transmission Capacity of the “Ether” and Wire in Electrocommunications

      • V. A. Kotel’nikov
      Pages 27-45

  4. Sampling, Wavelets, and the Uncertainty Principle

    1. Front Matter

      Pages 47-47
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    2. Wavelets and Sampling

      • Gilbert G. Walter
      Pages 49-71

    3. Embeddings and Uncertainty Principles for Generalized Modulation Spaces

      • J. A. Hogan, J. D. Lakey
      Pages 73-105

    4. Sampling Theory for Certain Hilbert Spaces of Bandlimited Functions

      • Jean-Pierre Gabardo
      Pages 107-134

    5. Shannon-Type Wavelets and the Convergence of Their Associated Wavelet Series

      • Ahmed I. Zayed
      Pages 135-152

  6. Sampling Tools and Applications

    1. Front Matter

      Pages 245-245
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    2. Fast Fourier Transforms for Nonequispaced Data: A Tutorial

      • Daniel Potts, Gabriele Steidl, Manfred Tasche
      Pages 247-270

    3. Efficient Minimum Rate Sampling of Signals with Frequency Support over Non-Commensurable Sets

      • Cormac Herley, Ping Wah Wong
      Pages 271-291

    4. Finite-and Infinite-Dimensional Models for Oversampled Filter Banks

      • Thomas Strohmer
      Pages 293-315

    5. Statistical Aspects of Sampling for Noisy and Grouped Data

      • M. Pawlak, U. Stadtmüller
      Pages 317-342

    6. Reconstruction of MRI Images from Non-Uniform Sampling and Its Application to Intrascan Motion Correction in Functional MRI

      • Marc Bourgeois, Frank T. A. W. Wajer, Dirk van Ormondt, Danielle Graveron-Demilly
      Pages 343-363
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Keywords

About this book

Sampling is a fundamental topic in the engineering and physical sciences. This new edited book focuses on recent mathematical methods and theoretical developments, as well as some current central applications of the Classical Sampling Theorem. The Classical Sampling Theorem, which originated in the 19th century, is often associated with the names of Shannon, Kotelnikov, and Whittaker; and one of the features of this book is an English translation of the pioneering work in the 1930s by Kotelnikov, a Russian engineer. Following a technical overview and Kotelnikov's article, the book includes a wide and coherent range of mathematical ideas essential for modern sampling techniques. These ideas involve wavelets and frames, complex and abstract harmonic analysis, the Fast Fourier Transform (FFT),and special functions and eigenfunction expansions. Some of the applications addressed are tomography and medical imaging. Topics:. Relations between wavelet theory, the uncertainty principle, and sampling; . Multidimensional non-uniform sampling theory and algorithms;. The analysis of oscillatory behavior through sampling;. Sampling techniques in deconvolution;. The FFT for non-uniformly distributed data; . Filter design and sampling; . Sampling of noisy data for signal reconstruction;. Finite dimensional models for oversampled filter banks; . Sampling problems in MRI. Engineers and mathematicians working in wavelets, signal processing, and harmonic analysis, as well as scientists and engineers working on applications as varied as medical imaging and synthetic aperture radar, will find the book to be a modern and authoritative guide to sampling theory.

Reviews

"The introduction (Chapter 1) gives an excellent overview of the history and development of sampling theory. It shows that the WSK sampling theory has roots in many classical areas of mathematics, such as harmonic analysis, number theory, and interpolation theory. Many famous mathematicians, such as Cauchy, Borel, Hadamard, and de la Vallee-Poussin contributed directly or indirectly to its development. The introduction then proceeds to show how sampling theory is connected to more recent topics in mathematical analysis, such as wavelets, Gabor systems, density theorems, frames, and sampling in locally compact abelian groups."

—Mathematical Reviews

"Engineers and mathematicians working in wavelets, signal processing, and harmonic analysis, as well as scientists and engineers working on applications as varied as medical imaging and synthetic aperture radar, will find the book to be a modern and authoritative guide to sampling theory."

—Publicationes Mathematicae

Editors and Affiliations

  • Department of Mathematics, University of Maryland, College Park, USA

    John J. Benedetto

  • Departamento de Electronica e Telecommunicacoes, Universidade de Aveiro, Aveiro, Portugal

    Paulo J. S. G. Ferreira

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