Authors:
- First unified presentation of Fourier theory and corresponding algorithms
- Covers many recent highly recognized developments in numerical Fourier analysis
- The code of most of the presented algorithms is available in public software packages of the authors
Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
About this book
This book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods.
It starts with a detailed discussion of classical Fourier theory to enable readers to grasp the construction and analysis of advanced fast Fourier algorithms introduced in the second part, such as nonequispaced and sparse FFTs in higher dimensions.
Lastly, it contains a selection of numerical applications, including recent research results on nonlinear function approximation by exponential sums.
The code of most of the presented algorithms is available in the authors’ public domain software packages.
Students and researchers alike benefit from this unified presentation of Fourier theory and corresponding algorithms.Keywords
- fourier analysis
- fourier series
- fourier transforms
- discrete fourier transforms
- fast fourier transforms
- multidimensional fourier methods
- fft
- sparse fft
- chebyshev methods
- discrete cosine transforms
- discrete polynomial transforms
- nonequispaced fft
- high-dimensional fft
- fft on rank-1 lattices
- fast spherical fourier transform
- prony methods
- phase retrieval
- information and communication, circuits
- matrix theory
Authors and Affiliations
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University of Göttingen, Göttingen, Germany
Gerlind Plonka
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Chemnitz University of Technology, Chemnitz, Germany
Daniel Potts
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TU Kaiserslautern, Kaiserslautern, Germany
Gabriele Steidl
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University of Rostock, Rostock, Germany
Manfred Tasche
Bibliographic Information
Book Title: Numerical Fourier Analysis
Authors: Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche
Series Title: Applied and Numerical Harmonic Analysis
DOI: https://doi.org/10.1007/978-3-030-04306-3
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
eBook ISBN: 978-3-030-04306-3Published: 05 February 2019
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number: 1
Number of Pages: XVI, 618
Number of Illustrations: 21 b/w illustrations, 30 illustrations in colour
Topics: Abstract Harmonic Analysis, Numerical Analysis, Information and Communication, Circuits, Linear and Multilinear Algebras, Matrix Theory