Modern Sampling Theory

Mathematics and Applications
Softcover Nachdruck of the original 1. Auflage 2001
ISBN: 978-1-4612-6632-7
Verlag: Birkhäuser Boston

Buch, Englisch, 419 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 657 g

Reihe: Applied and Numerical Harmonic Analysis

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:. 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.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Ferreira, Paulo J. S. G.

Benedetto, John J.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Signalverarbeitung, Bildverarbeitung, Scanning
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse

Inhaltsverzeichnis

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.