harmonic analysis

harmonic analysis
A study of the representation of functions or signals as the superposition of basic waves, involving the notions of harmonic functions, trigonometric series, Fourier series, Fourier transforms, almost periodic functions, and others.

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  • Harmonic analysis — is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms. The basic waves are called harmonics… …   Wikipedia

  • harmonic analysis — n. 1. the study of Fourier series 2. the act of breaking a periodic function into components, each expressed as a sine or cosine function …   English World dictionary

  • harmonic analysis — Math. 1. the calculation of Fourier series and their generalization. 2. the study of Fourier series and their generalization. Also called Fourier analysis. [1865 70] * * * ▪ mathematics       mathematical procedure for describing and analyzing… …   Universalium

  • harmonic analysis — noun analysis of a periodic function into a sum of simple sinusoidal components • Syn: ↑Fourier analysis • Hypernyms: ↑analysis * * * noun : the approximate expression of a periodic function known only for some values of the independent variable… …   Useful english dictionary

  • harmonic analysis — harmoninė analizė statusas T sritis fizika atitikmenys: angl. harmonic analysis; harmonical analysis vok. harmonische Analyse, f rus. гармонический анализ, m pranc. analyse harmonique, f …   Fizikos terminų žodynas

  • harmonic analysis — noun Date: 1867 the expression of a periodic function as a sum of sines and cosines and specifically by a Fourier series …   New Collegiate Dictionary

  • harmonic analysis — harmon′ic anal′ysis n. math. the calculation or study of Fourier series and their generalization • Etymology: 1865–70 …   From formal English to slang

  • Spherical harmonic analysis — Harmonic Har*mon ic (h[aum]r*m[o^]n [i^]k), Harmonical Har*mon ic*al ( [i^]*kal), a. [L. harmonicus, Gr. armoniko s; cf. F. harmonique. See {Harmony}.] 1. Concordant; musical; consonant; as, harmonic sounds. [1913 Webster] Harmonic twang! of… …   The Collaborative International Dictionary of English

  • Noncommutative harmonic analysis — In mathematics, noncommutative harmonic analysis is the field in which results from Fourier analysis are extended to topological groups which are not commutative. Since for locally compact abelian groups have a well understood theory, Pontryagin… …   Wikipedia

  • List of harmonic analysis topics — This is a list of harmonic analysis topics, by Wikipedia page. See also list of Fourier analysis topics and list of Fourier related transforms, which are more directed towards the classical Fourier series and Fourier transform of mathematical… …   Wikipedia

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