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Mathematical analysis
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=== Harmonic analysis === {{Main|Harmonic analysis}} Harmonic analysis is a branch of mathematical analysis concerned with the representation of [[function (mathematics)|function]]s and [[signal]]s as the superposition of basic [[wave]]s. This includes the study of the notions of [[Fourier series]] and [[Fourier transform]]s ([[Fourier analysis]]), and of their generalizations. Harmonic analysis has applications in areas as diverse as [[music theory]], [[number theory]], [[representation theory]], [[signal processing]], [[quantum mechanics]], [[tidal analysis]], and [[neuroscience]].
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