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
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Rajula Srivastava, for contributions in harmonic analysis and analytic number theory, including contributions to the problem of counting rational points near smooth manifolds.
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Alex Cramer, HollywoodReporter, 6 Apr. 2025
Perhaps, Maynard thought, tools from another area of math called harmonic analysis might be useful.
—Jordana Cepelewicz, WIRED, 4 Aug. 2024
Tower of Dreams The conjecture’s resolution is a seismic shift for the field of harmonic analysis, which studies the details of the Fourier transform.
—Joseph Howlett, Quanta Magazine, 14 Mar. 2025
Guth studied it on and off for a few years, only to realize that his techniques from harmonic analysis wouldn’t work.
—Jordana Cepelewicz, WIRED, 4 Aug. 2024
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
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
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Alex Cramer, HollywoodReporter, 6 Apr. 2025
Perhaps, Maynard thought, tools from another area of math called harmonic analysis might be useful.
—Jordana Cepelewicz, WIRED, 4 Aug. 2024
Tower of Dreams The conjecture’s resolution is a seismic shift for the field of harmonic analysis, which studies the details of the Fourier transform.
—Joseph Howlett, Quanta Magazine, 14 Mar. 2025
Guth studied it on and off for a few years, only to realize that his techniques from harmonic analysis wouldn’t work.
—Jordana Cepelewicz, WIRED, 4 Aug. 2024
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
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
Cite this Entry
“Harmonic analysis.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/harmonic%20analysis. Accessed 23 Jul. 2025.
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