harmonic analysis

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harmonic analysis

n.
The study of functions given by a Fourier series or analogous representations, such as periodic functions and functions on topological groups.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

harmonic analysis

n
1. (Mathematics) the representation of a periodic function by means of the summation and integration of simple trigonometric functions
2. (Mathematics) the study of this means of representation
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

harmon′ic anal′ysis


n.
the calculation or study of Fourier series and their generalization.
[1865–70]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.harmonic analysis - analysis of a periodic function into a sum of simple sinusoidal components
analysis - a branch of mathematics involving calculus and the theory of limits; sequences and series and integration and differentiation
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References in periodicals archive ?
However, one limitation of the Fourier theory is its accuracy, which is deficient for extreme low-temperature or ultra-short-pulse thermal heating in temporal-spatial scale [3-6].
The text covers sets and functions, Lebesgue measure, measurable sets, Borel sets, sets of measure zero, the integral, measurable functions, convergence theorems, convergence in mean, Fourier theory, calculus, change of variables, differentiation of integrals, integration of derivatives, and general measures.
In the Fourier transform literature, the Heisenberg Uncertainty Principle is derived from a general theorem of Fourier theory called the Uncertainty Theorem [7].

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