New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis.The first four chapters of the text serve as an introduction to classical Fourier analysis in ...

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, inclu...