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Library | Materyal Türü | Barkod | Yer Numarası | Durum |
|---|---|---|---|---|
Searching... Pamukkale Merkez Kütüphanesi | Kitap | 0061237 | QA276.6M6891 2001 | Searching... Unknown |
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Özet
Özet
Sampling is a fundamental topic in the engineering and physicalsciences. This new edited book focuses on recent mathematical methodsand theoretical developments, as well as some current centralapplications of the Classical Sampling Theorem. The Classical SamplingTheorem, whichoriginated in the 19th century, is often associated with the names ofShannon, Kotelnikov, and Whittaker; and one of the features of thisbook is an English translation of the pioneering work in the 1930s byKotelnikov, a Russian engineer.Following a technical overview and Kotelnikov's article, the bookincludes a wide and coherent range of mathematical ideas essential formodern 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 theapplications addressed are tomography and medical imaging.Topics:. Relations between wavelet theory, the uncertainty principle,and sampling; . Multidimensional non-uniform sampling theory andalgorithms;. The analysis of oscillatory behavior through sampling;.Sampling techniques in deconvolution;. The FFT for non-uniformlydistributed data;. Filter design and sampling;. Sampling of noisy data for signal reconstruction;. Finitedimensional 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 onapplications as varied as medical imaging and synthetic apertureradar, will find the book to be a modern and authoritative guide tosampling theory.
Table of Contents
| 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 |