Modern Sampling Theory: Mathematics and Applications

ISBN-13: 9780817640231 / Angielski / Twarda / 2001 / 419 str.

Paulo J. S. G. Ferreira; John J. Bendetto; J. S. G. Ferreura

Opis

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 and features: - 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.

Recenzje

"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

Spis treści

Introduction, On the transmission capacity of the 'ether' and wire in electrocommunications, Part I: Sampling, wavelets, and the uncertainty principle, Wavelets and sampling, Embeddings and uncertainty principles for generalized modulation spaces, Sampling theory for certain hilbert spaces of bandlimited functions, Shannon-type wavelets and the convergence of their associated wavelet series, Part II: Sampling topics from mathematical analysis, Non-uniform sampling in higher dimensions: From trigonometric polynomials to bandlimited functions, The analysis of oscillatory behavior in signals through their samples, Residue and sampling techniques in deconvolution, Sampling theorems from the iteration of low order differential operators, Approximation of continuous functions by Rogosinski-Type sampling series, Part III: Sampling tools and applications, Fast fourier transforms for nonequispaced data: A tutorial, Efficient minimum rate sampling of signals with frequency support over non-commensurable sets, Finite and infinite-dimensional models for oversampled filter banks, Statistical aspects of sampling for noisy and grouped data, Reconstruction of MRI images from non-uniform sampling, application to Intrascan motion correction in functional MRI, Efficient sampling of the rotation invariant radon transform