Discrete Fourier Analysis

Abstract

This textbook presents basic notions and techniques of Fourier analysisin discrete settings. Written in a concise style, it is interlacedwith 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 andculminates in a section on pseudo-differential operators, providinga lucid introduction to this advanced topic in analysis. Some measuretheory language is used, although most of this part is accessibleto students familiar with an undergraduate course in real analysis.Discrete Fourier Analysis is aimed at advanced undergraduate and graduatestudents in mathematics and applied mathematics. Enhanced with exercises,it will be an excellent resource for the classroom as well as forself-study.