Applied and Numerical Harmonic Analysis

Modern Sampling Theory

Mathematics and Applications

Editors: Benedetto, John J., Ferreira, Paulo J.S.G. (Eds.)

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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


Table of contents (17 chapters)

  • Introduction

    Benedetto, John J. (et al.)

    Pages 1-26

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

    Kotel’nikov, V. A.

    Pages 27-45

  • Wavelets and Sampling

    Walter, Gilbert G.

    Pages 49-71

  • Embeddings and Uncertainty Principles for Generalized Modulation Spaces

    Hogan, J. A. (et al.)

    Pages 73-105

  • Sampling Theory for Certain Hilbert Spaces of Bandlimited Functions

    Gabardo, Jean-Pierre

    Pages 107-134

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-1-4612-0143-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $249.00
price for USA
  • ISBN 978-0-8176-4023-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $199.00
price for USA
  • ISBN 978-1-4612-6632-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Modern Sampling Theory
Book Subtitle
Mathematics and Applications
Editors
  • John J. Benedetto
  • Paulo J.S.G. Ferreira
Series Title
Applied and Numerical Harmonic Analysis
Copyright
2001
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-0143-4
DOI
10.1007/978-1-4612-0143-4
Hardcover ISBN
978-0-8176-4023-1
Softcover ISBN
978-1-4612-6632-7
Series ISSN
2296-5009
Edition Number
1
Number of Pages
XVI, 419
Topics