Fourier transform
noun
: any of various functions (such as F(u)) that under suitable conditions can be obtained from given functions (such as f(x)) by multiplying by eiux and integrating over all values of x and that in scientific instrumentation describe the dependence of the average of a series of measurements (as of a spectrum) on a quantity of interest (such as brightness) especially of a very small magnitude
called also Fourier transformation
Examples of Fourier transform in a Sentence
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The researchers used advanced techniques, including gas chromatography and Fourier transform infrared spectroscopy, to determine what the tunic was made from.
—
Marco Rubio, Newsweek, 1 Nov. 2024
The Fourier transform goes back and forth between these two sides.
—Erica Klarreich, Quanta Magazine, 19 July 2024
For those of you who don’t remember your college signal processing, a Fourier transform is a mathematical tool that turns a signal in time, such as the oscillation of voltage in a circuit, into a signal in frequency.
—IEEE Spectrum, 22 Dec. 2023
The Fourier transform has played a fundamental role in solving differential equations, expressing quantum mechanical ideas like the Heisenberg uncertainty principle, and analyzing and processing signals — making things like modern mobile phones possible.
—Quanta Magazine, 12 Sep. 2023
This later inspired mathematicians to develop a hierarchy of conjectures about the higher-dimensional behavior of the Fourier transform.
—Jordana Cepelewicz, Quanta Magazine, 11 July 2023
As a result, the Fourier transform has led directly to a number of applications in scientific research and technology.
—Quanta Magazine, 13 Oct. 2021
Similar to the discrete Fourier transform, the DCT converts a signal or image from the spatial domain (a matrix of pixels) to the frequency domain (in which images are represented by mathematical functions).
—Jae Jeong Hwang, IEEE Spectrum, 1 Apr. 2023
Performing a Fourier transform involves representing a signal in terms of its sines and cosines of various frequencies, Stern says.
—Kat Friedrich, Popular Mechanics, 13 Feb. 2023
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Marco Rubio, Newsweek, 1 Nov. 2024
The Fourier transform goes back and forth between these two sides.
—Erica Klarreich, Quanta Magazine, 19 July 2024
For those of you who don’t remember your college signal processing, a Fourier transform is a mathematical tool that turns a signal in time, such as the oscillation of voltage in a circuit, into a signal in frequency.
—IEEE Spectrum, 22 Dec. 2023
The Fourier transform has played a fundamental role in solving differential equations, expressing quantum mechanical ideas like the Heisenberg uncertainty principle, and analyzing and processing signals — making things like modern mobile phones possible.
—Quanta Magazine, 12 Sep. 2023
This later inspired mathematicians to develop a hierarchy of conjectures about the higher-dimensional behavior of the Fourier transform.
—Jordana Cepelewicz, Quanta Magazine, 11 July 2023
As a result, the Fourier transform has led directly to a number of applications in scientific research and technology.
—Quanta Magazine, 13 Oct. 2021
Similar to the discrete Fourier transform, the DCT converts a signal or image from the spatial domain (a matrix of pixels) to the frequency domain (in which images are represented by mathematical functions).
—Jae Jeong Hwang, IEEE Spectrum, 1 Apr. 2023
Performing a Fourier transform involves representing a signal in terms of its sines and cosines of various frequencies, Stern says.
—Kat Friedrich, Popular Mechanics, 13 Feb. 2023
Dictionary Entries Near Fourier transform
Cite this Entry
“Fourier transform.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/Fourier%20transform. Accessed 30 Dec. 2024.
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