Modern Sampling Theory

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 for all researchers and professionals in applied math and engineering working in fourier analysis, wavelets, signal processing and time-frequency analysis.

"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

Contenu
1 Introduction.- 1.1 The Classical Sampling Theorem.- 1.2 Non-Uniform Sampling and Frames.- 1.3 Outline of the Book.- 2 On the Transmission Capacity of the Ether and Wire in Electrocommunications.- I Sampling, Wavelets, and the Uncertainty Principle.- 3 Wavelets and Sampling.- 4 Embeddings and Uncertainty Principles for Generalized Modulation Spaces.- 5 Sampling Theory for Certain Hilbert Spaces of Bandlimited Functions.- 6 Shannon-Type Wavelets and the Convergence of Their Associated Wavelet Series.- II Sampling Topics from Mathematical Analysis.- 7 Non-Uniform Sampling in Higher Dimensions: From Trigonometric Polynomials to Bandlimited Functions.- 8 The Analysis of Oscillatory Behavior in Signals Through Their Samples.- 9 Residue and Sampling Techniques in Deconvolution.- 10 Sampling Theorems from the Iteration of Low Order Differential Operators.- 11 Approximation of Continuous Functions by RogosinskiType Sampling Series.- III Sampling Tools and Applications.- 12 Fast Fourier Transforms for Nonequispaced Data: A Tutorial.- 13 Efficient Minimum Rate Sampling of Signals with Frequency Support over Non-Commensurable Sets.- 14 Finite-and Infinite-Dimensional Models for Oversampled Filter Banks.- 15 Statistical Aspects of Sampling for Noisy and Grouped Data.- 16 Reconstruction of MRI Images from Non-Uniform Sampling and Its Application to Intrascan Motion Correction in Functional MRI.- 17 Efficient Sampling of the Rotation Invariant Radon Transform.- References.