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Numerical Fourier Analysis

  • Gerlind Plonka
  • Daniel Potts
  • Gabriele Steidl
  • Manfred Tasche
Book

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xvi
    PDF
  2. Fourier Series
    Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche
    Pages 1-59
  3. Fourier Transforms
    Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche
    Pages 61-106
  4. Discrete Fourier Transforms
    Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche
    Pages 107-157
  5. Multidimensional Fourier Methods
    Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche
    Pages 159-230
  6. Fast Fourier Transforms
    Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche
    Pages 231-303
  7. Chebyshev Methods and Fast DCT Algorithms
    Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche
    Pages 305-376
  8. Fast Fourier Transforms for Nonequispaced Data
    Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche
    Pages 377-419
  9. High-Dimensional FFT
    Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche
    Pages 421-448
  10. Numerical Applications of DFT
    Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche
    Pages 449-521
  11. Prony Method for Reconstruction of Structured Functions
    Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche
    Pages 523-573
  12. Back Matter
    Pages 575-618
    PDF

About this book

Introduction

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

Authors and affiliations

  • Gerlind Plonka
    • 1
  • Daniel Potts
    • 2
  • Gabriele Steidl
    • 3
  • Manfred Tasche
    • 4
  1. 1.University of GöttingenGöttingenGermany
  2. 2.Chemnitz University of TechnologyChemnitzGermany
  3. 3.TU KaiserslauternKaiserslauternGermany
  4. 4.University of RostockRostockGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-04306-3
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-04305-6
  • Online ISBN 978-3-030-04306-3
  • Series Print ISSN 2296-5009
  • Series Online ISSN 2296-5017
  • Buy this book on publisher's site