„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
Modern Sampling Theory
Mathematics and Applications
herausgegeben von John J. Benedetto und Paulo J.S.G. Ferreirasciences. 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.
