Applied and Numerical Harmonic Analysis

Mathematics and Applications

By: John J. Benedetto (Editor), Paulo J.S.G. Ferreira (Editor)

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Hardcover | 16 February 2001

At a Glance

Hardcover
438 Pages

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16.51 x 25.4 x 3.18

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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. 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.

Industry Reviews

"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

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You Can Find This Book In

Non-Fiction Mathematics Probability & Statistics Applied Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Engineering & Technology Technology in General Engineering in General Numerical Analysis

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Paperback

Published: 23rd October 2012

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Introduction
On the transmission capacity of the "ether" and wire in electrocommunications
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
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
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
Table of Contents provided by Publisher. All Rights Reserved.

Applied and Numerical Harmonic Analysis

Mathematics and Applications

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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