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Jean-Baptiste Joseph Fourier (/ ˈ f ʊr i eɪ,-i ər /; [1] French: [ʒɑ̃ batist ʒozɛf fuʁje]; 21 March 1768 – 16 May 1830) was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems of heat transfer and vibrations.
Fourier series, a weighted sum of sinusoids having a common period, the result of Fourier analysis of a periodic function; Fourier analysis, the description of functions as sums of sinusoids; Fourier transform, the type of linear canonical transform that is the generalization of the Fourier series
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex-valued function of frequency.
François Marie Charles Fourier (/ ˈ f ʊr i eɪ,-i ər /; [1] French: [ʃaʁl fuʁje]; 7 April 1772 – 10 October 1837) was a French philosopher, an influential early socialist thinker, and one of the founders of utopian socialism. [2]
In the sciences and engineering, the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis.
Fourierism is the set of ideas first put forward by French utopian socialist François Marie Charles Fourier (1772–1837).. Fourierism (/ ˈ f ʊər i ə r ɪ z əm /) [1] is the systematic set of economic, political, and social beliefs first espoused by French intellectual Charles Fourier (1772–1837).
A Fourier series (/ ˈ f ʊr i eɪ,-i ər / [1]) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. [2] By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are ...
List of Fourier-related transforms; Fourier transform on finite groups; Fractional Fourier transform; Continuous Fourier transform; Fourier operator; Fourier inversion theorem; Sine and cosine transforms; Parseval's theorem; Paley–Wiener theorem; Projection-slice theorem; Frequency spectrum