Modern Sampling Theory: Mathematics and Applications

Edited by: John J. Benedetto and Paulo J. S. G. Ferreira.

Publisher: Birkhauser Boston, Applied and Numerical Harmonic Analysis Series, 2001.

Table of Contents, Preface, List of Contributors (Postscript).

Table of Contents, Preface, List of Contributors (PDF).

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, Kotel'nikov, and Whittaker; and one of the features of this book is an English translation of the pioneering work in the 1930s by Kotel'nikov, a Russian engineer.

Vladimir Alexandrovitch Kotel'nikov, whose 90th birthday in 1998 was recognized by the IEEE Information Theory Society as part of its annual symposium, was awarded the IEEE Alexander Graham Bell Medal in Moscow, on 17 May 2000, for fundamental contributions to signal theory. He also worked on jet technology, devices for the control of rocket trajectories, code systems, and radio and radar planetology, both earthbound and from spacecraft. As IEEE President Eisenstein said during his address in the cerimony, "over the years the West had its Shannon; and the East had its Kotel'nikov".

Following a technical overview and Kotel'nikov'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.