Numerical Fourier analysis / Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche.
2023
QA403.5 .P56 2023
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Details
Title
Numerical Fourier analysis / Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche.
Author
Plonka, Gerlind, author.
Edition
Second edition.
ISBN
9783031350054 (electronic bk.)
3031350057 (electronic bk.)
3031350049
9783031350047
3031350057 (electronic bk.)
3031350049
9783031350047
Published
Cham : Birkhäuser, [2023]
Copyright
©2023
Language
English
Description
1 online resource (xviii, 664 pages) : illustrations (some color).
Item Number
10.1007/978-3-031-35005-4 doi
Call Number
QA403.5 .P56 2023
Dewey Decimal Classification
515/.2433
Summary
New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis. The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions. This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others. Numerical Fourier Analysis will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed November 16, 2023).
Series
Applied and numerical harmonic analysis, 2296-5009
Available in Other Form
Print version: 9783031350047
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Table of Contents
Fourier series
Fourier transforms
Discrete Fourier transforms
Multidimensional Fourier methods
Fast Fourier transforms
Chebyshev methods and fast DCT algorithms
Fast Fourier transforms for nonequispaced data
High dimensional FFT
Numerical applications of DFT
Prony method for reconstruction of structured functions.
Fourier transforms
Discrete Fourier transforms
Multidimensional Fourier methods
Fast Fourier transforms
Chebyshev methods and fast DCT algorithms
Fast Fourier transforms for nonequispaced data
High dimensional FFT
Numerical applications of DFT
Prony method for reconstruction of structured functions.