Modern Sampling Theory

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.

---

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.