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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
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
. 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
Content Level »Professional/practitioner
Keywords »Fourier transform - Modulation - Shannon - communication - fast Fourier transform - fast Fourier transform (FFT) - harmonic analysis - signal analysis - signal processing
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