Numerical Fourier Analysis

✍ Scribed by G. Plonka, D. Potts, G. Steidl, M. Tasche

Publisher: Birkhäuser
Year: 2018
Tongue: English
Leaves: 624
Series: Applied and Numerical Harmonic Analysis
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

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

✦ Subjects

Fourier Analysis, Numerical Analysis

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