Overview
- Offers the first unified presentation of Fourier analysis and corresponding numerical algorithms
- Discusses many recent research developments in numerical Fourier analysis
- Explores application in signal processing, data analysis, and other rapidly emerging areas
Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)
Buy print copy
About this book
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.
Keywords
Table of contents (10 chapters)
Authors and Affiliations
About the authors
Daniel Potts received his Ph.D. degree in mathematics from the University of Rostock in 1998.He held a research position at the University of Lübeck from 1996 to 2005, where he obtained his Habilitation degree in 2004. Since 2005 he works as a Full Professor at the TU Chemnitz. His research focuses on applied analysis, in particular computational harmonic analysis, and applications in scientific computing.
Gabriele Steidl received the Ph.D. degree in mathematics and the Habilitation degree from the University of Rostock in 1988 and 1991, respectively. She had positions as Associated Professor for mathematics at the TU Darmstadt and as Full Professor at the University of Mannheim and the TU Kaiserslautern, where she also worked as consultant of the Fraunhofer ITWM Kaiserslautern. Since 2020 she is Full Professor at the TU Berlin. In 2022 she became a SIAM Fellow. Her research interests include harmonic analysis, optimization, inverse problems and machine learning with applications in image and signal processing.
Manfred Tasche received the Ph.D. degree in mathematics and the Habilitation degree from the University of Rostock in 1966 and 1976, respectively. He was Associate Professor and later Full Professor for Analysis and Numerical Mathematics at the University of Rostock from 1978 to 1993. Until 2008, he worked as substitute Professor and Assistant Professor at the University of Lübeck and the University of Rostock. Since 2008 he is retired. His research focuses on numerical analysis and approximation, Fourier analysis and applications in signal processing.
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/10.1007/978-3-031-35005-4
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-35004-7Published: 09 November 2023
Softcover ISBN: 978-3-031-35007-8Due: 22 November 2024
eBook ISBN: 978-3-031-35005-4Published: 08 November 2023
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number: 2
Number of Pages: XVIII, 664
Number of Illustrations: 22 b/w illustrations, 30 illustrations in colour
Topics: Fourier Analysis, Abstract Harmonic Analysis, Numerical Analysis, Mathematical Applications in Computer Science, Linear Algebra