Modern Sampling Theory: Mathematics and Applications

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.