Fourier transform


: 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

Recent Examples on the Web 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 Wavelets came about as a kind of update to an enormously useful mathematical technique known as the Fourier transform. Quanta Magazine, 13 Oct. 2021 Ross’ study uses technology called Fourier transform infrared spectroscopy (FTIR) that became available in just the past few years. Justine Calma, The Verge, 12 Jan. 2021 See More

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'Fourier transform.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

First Known Use

1923, in the meaning defined above

Time Traveler
The first known use of Fourier transform was in 1923

Dictionary Entries Near Fourier transform

Cite this Entry

“Fourier transform.” Dictionary, Merriam-Webster, Accessed 22 Feb. 2024.

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