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Numerical Fourier Analysis

Author: Gerlind Plonka

Publisher: Springer

Published: 2019-02-05

Total Pages: 624

ISBN-13: 3030043061

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.

Methods of Applied Fourier Analysis

Author: Jayakumar Ramanathan

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 334

ISBN-13: 1461217563

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Fourier Analysis on Finite Abelian Groups

Author: Bao Luong

Publisher: Springer Science & Business Media

Published: 2009-08-14

Total Pages: 167

ISBN-13: 0817649166

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This unified, self-contained book examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform to finite Abelian groups. With countless examples and unique exercise sets at the end of each section, Fourier Analysis on Finite Abelian Groups is a perfect companion to a first course in Fourier analysis. This text introduces mathematics students to subjects that are within their reach, but it also has powerful applications that may appeal to advanced researchers and mathematicians. The only prerequisites necessary are group theory, linear algebra, and complex analysis.

Computational Frameworks for the Fast Fourier Transform

Author: Charles Van Loan

Publisher: SIAM

Published: 1992-01-01

Total Pages: 285

ISBN-13: 0898712858

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The author captures the interplay between mathematics and the design of effective numerical algorithms.

The Fast Fourier Transform and Its Applications

Author: E. Oran Brigham

Publisher: Pearson

Published: 1988

Total Pages: 474

ISBN-13:

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The Fast Fourier Transform (FFT) is a mathematical method widely used in signal processing. This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field.

Fourier Analysis and Applications

Author: Claude Gasquet

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 434

ISBN-13: 1461215986

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The object of this book is two-fold -- on the one hand it conveys to mathematical readers a rigorous presentation and exploration of the important applications of analysis leading to numerical calculations. On the other hand, it presents physics readers with a body of theory in which the well-known formulae find their justification. The basic study of fundamental notions, such as Lebesgue integration and theory of distribution, allow the establishment of the following areas: Fourier analysis and convolution Filters and signal analysis time-frequency analysis (gabor transforms and wavelets). The whole is rounded off with a large number of exercises as well as selected worked-out solutions.

Fourier Analysis of Numerical Approximations of Hyperbolic Equations

Author: R. Vichnevetsky

Publisher: SIAM

Published: 1982-01-01

Total Pages: 146

ISBN-13: 0898713927

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This book provides useful reference material for those concerned with the use of Fourier analysis and computational fluid dynamics.

Discrete Fourier Analysis

Author: M. W. Wong

Publisher: Springer Science & Business Media

Published: 2011-05-30

Total Pages: 175

ISBN-13: 3034801165

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This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis. The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis. Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study.