Harmonic analysis is the foundation for much of modern mathematical analysis. Based on the idea of breaking up an arbitrary function into simple component functions, harmonic analysis has become a powerful and pervasive part of mathematics. Image processing, signal compression, partial differential equations, control theory, and many other essential parts of engineering and applied mathematics are studied using aspects of harmonic analysis. Fourier series, Fourier transforms, pseudodifferential operators, and wavelets are all aspects of the subject that find application to real-world problems. The subject of this article acquaints the reader with the fundamental components of this type of analysis. Minimal background is required to come away with an appreciation of the power and diversity of the methodology. WIREs Comp Stat 2011 3 163–167 DOI: 10.1002/wics.143

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