Numerical Fourier Analysis
Harmonic analysis Numerical analysis Mathematics Matrix theory Abstract Harmonic Analysis Information and Communication, Circuits Linear and Multilinear Algebras, Matrix Theory
Imprint: Birkhäuser
2018
1st ed. 2018.
EISBN 3030043061
Fourier series.
Fourier transforms.
Discrete Fourier transforms.
Multidimensional Fourier methods.
Fast Fourier transforms.
Chebyshev methods and fast DCT algorithms.
Fast Fourier transforms for nonequispaced data.
High dimensional FFT.
Numerical applications of DFT.
Prony method for reconstruction of structured functions.
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.
Fourier transforms.
Discrete Fourier transforms.
Multidimensional Fourier methods.
Fast Fourier transforms.
Chebyshev methods and fast DCT algorithms.
Fast Fourier transforms for nonequispaced data.
High dimensional FFT.
Numerical applications of DFT.
Prony method for reconstruction of structured functions.
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.
