harmonic analysis

American  

noun

Mathematics.

1. the calculation of Fourier series and their generalization.

2. the study of Fourier series and their generalization.

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harmonic analysis British  

noun

1. the representation of a periodic function by means of the summation and integration of simple trigonometric functions

2. the study of this means of representation

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harmonic analysis Scientific  

1. The study of functions given by a Fourier series or analogous representations, such as periodic functions and functions on topological groups.

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Etymology

Origin of harmonic analysis

First recorded in 1865–70

Example Sentences

Modulations can make harmonic analysis much more challenging, so try to become comfortable analyzing easier pieces before tackling pieces with modulations.

From Literature

Dr. Flores studies mathematical physics, partial differential equations, and harmonic analysis, so it is fitting that the theorem she chose to share on the podcast has a physics flavor.

From Scientific American

Inspired by subsequent developments in Galois’s theory, Langlands’ approach allowed researchers to translate algebra problems into the ‘language’ of harmonic analysis, the branch of mathematics that breaks complex waveforms down into simpler, sinusoidal building blocks.

From Nature

Thomson, D. J. Spectrum estimation and harmonic analysis.

From Nature

Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps.

From Nature