harmonic analysis

noun

: the expression of a periodic function as a sum of sines and cosines and specifically by a Fourier series

Examples of harmonic analysis in a Sentence

Recent Examples on the Web

Larry Guth’s expertise in harmonic analysis gave him a fresh perspective on a number theory problem that had resisted proof for decades. —Jordana Cepelewicz, WIRED, 4 Aug. 2024

Larry Guth, an expert in harmonic analysis who was at the same conference, just happened to already be thinking along similar lines. —Jordana Cepelewicz, Quanta Magazine, 15 July 2024

Guth studied it on and off for a few years, only to realize that his techniques from harmonic analysis wouldn’t work. —Jordana Cepelewicz, Quanta Magazine, 15 July 2024

In 1874 in the United States, William Ferrel, a mathematician with the Coast and Geodetic Survey, developed a similar harmonic analysis and prediction device that used 19 harmonic constituents. —IEEE Spectrum, 2 June 2024

The proof refined techniques in harmonic analysis — a seemingly distant area of math that deals with representing arbitrarily complicated functions in terms of simple waves — to strengthen the bound. —Leila Sloman, Quanta Magazine, 9 Apr. 2024

Classical harmonic analysis, which forms the foundation for signal processing in the real world, is all about decomposing signals into sine waves of different frequencies and phases. —Quanta Magazine, 1 Apr. 2024

Professor Tao has authored more than 300 research papers on an amazingly wide swath of mathematics including harmonic analysis, partial differential equations, combinatorics, number theory, data science, random matrices and much more. —Quanta Magazine, 1 Feb. 2024

The conjecture turns out to have implications not only for geometry, but also for harmonic analysis and the study of partial differential equations. —Quanta Magazine, 23 Dec. 2023

Word History

First Known Use

1867, in the meaning defined above

Rhymes for harmonic analysis

• electrodialysis
• cryptanalysis
• urinalysis
• dialysis
• paralysis
• haemodialysis
• hemodialysis
• microanalysis
• psychoanalysis