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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.

Fourier analysis. --- Fourier analysis --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Analysis, Fourier --- Mathematics. --- Harmonic analysis. --- Partial differential equations. --- Numerical analysis. --- Fourier Analysis. --- Abstract Harmonic Analysis. --- Partial Differential Equations. --- Numerical Analysis. --- Mathematical analysis --- Differential equations, partial. --- Partial differential equations --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Differential equations, Partial.

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Wavelets (Mathematics). --- Signal processing --- Mathematics.

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This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015. The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover applications in probability, differential equations and time-frequency analysis. A focus on the synergies of pseudo-differential operators with applications, especially real-life applications, enhances understanding of the analysis and the usefulness of these operators.

Mathematics. --- Operator theory. --- Partial differential equations. --- Information theory. --- Differential geometry. --- Probabilities. --- Operator Theory. --- Partial Differential Equations. --- Differential Geometry. --- Probability Theory and Stochastic Processes. --- Information and Communication, Circuits. --- Pseudodifferential operators. --- Operators, Pseudodifferential --- Pseudo-differential operators --- Operator theory --- Differential equations, partial. --- Global differential geometry. --- Distribution (Probability theory. --- Math --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Geometry, Differential --- Partial differential equations --- Functional analysis --- Communication theory --- Communication --- Cybernetics --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Differential geometry --- Differential equations, Partial. --- Geometry, Differential.

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This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015. The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover applications in probability, differential equations and time-frequency analysis. A focus on the synergies of pseudo-differential operators with applications, especially real-life applications, enhances understanding of the analysis and the usefulness of these operators.

Differential geometry. Global analysis --- Operator theory --- Partial differential equations --- Differential equations --- Operational research. Game theory --- Probability theory --- Mathematics --- Information systems --- differentiaalvergelijkingen --- ICT (informatie- en communicatietechnieken) --- analyse (wiskunde) --- differentiaal geometrie --- waarschijnlijkheidstheorie --- stochastische analyse --- informatiesystemen --- wiskunde --- kansrekening --- geometrie

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Differential geometry. Global analysis --- Operator theory --- Partial differential equations --- differentiaalvergelijkingen --- analyse (wiskunde) --- differentiaal geometrie