Numerical Fourier Analysis

Description

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. 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