# harmonic analysis

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## harmonic analysis

[här′man·ik ə′nal·ə·səs]
(mathematics)
A study of functions by attempting to represent them as infinite series or integrals which involve functions from some particular well-understood family; it subsumes studying a function via its Fourier series.
(physics)
Any method of identifying and evaluating the harmonics that make up a complex waveform of sound pressure, voltage, current, or some other varying quantity.
References in periodicals archive ?
The special session on wavelet and frame theoretic methods in harmonic analysis and partial differential equations was held in Rochester, New York in September 2012.
The intertwining operator V has been exploited to initiate a quite new commutative harmonic analysis on the real line related to the differential-difference operator [LAMBDA] in which several analytic structures on R were generalized.
The harmonic analysis of the vibration assisted turning tool was carried out in order to get quantitative results of the analysis.
harmonic analysis aided by the artificial immune system.
The purpose of SAMPTA's is to bring together mathematicians and engineers interested in sampling theory and its applications to related fields (such as signal and image processing, coding theory, control theory, complex analysis, harmonic analysis, differential equations) to exchange recent advances and to discuss open problems.
Using harmonic analysis, the interpretation of statistical results presents the appearance of the primary and second sound.
It is well known that the conjugate harmonic functions play very important role in many areas of mathematics such as harmonic analysis, the theory of [H.
Introduction to harmonic analysis and gerneralized Gelfand pairs.
Using modern mathematical techniques from the fields of partial differential equations and harmonic analysis - many of which were developed during the last five to 50 years, and thus relatively new to mathematics - the mathematicians proved the global existence of classical solutions and rapid time decay to equilibrium for the Boltzmann equation with long-range interactions.
The article of Jaak Peetre brings to light some intriguing connections between invariant theory, multilinear and especially trilinear forms, hyperdeterminants, bounded symmetric domains and harmonic analysis, actions of Lie groups and weighted Bergman spaces including several interesting directions for further investigation.
The response of turning tool to the acting cutting forces (for which harmonic form is considered) is realized using harmonic analysis.
In fact, they conduct industrial studies using ETAP, which is a power-modelling software that enables them to do power system designs and studies, as well as harmonic analysis and relay coordination.

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