A state-of-the-art edited survey covering all aspects of sampling theory. Theory, methods and applications are discussed in authoritative expositions ranging from multi-dimensional signal analysis to wavelet transforms. The book is an essential up-to-date resource.

Inhalt

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