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Fourier analysis - translation to russian
.png?width=200 "Bass guitar time signal of open string A note (55 Hz).")
![functions]].](https://commons.wikimedia.org/wiki/Special:FilePath/Fourier Transform of bass guitar time signal.png?width=200 "functions]].")
общая лексика
гармонический анализ
анализ Фурье
физика
критерий Фурье
![The [[atomic orbital]]s of [[chemistry]] are partially described by [[spherical harmonic]]s, which can be used to produce Fourier series on the [[sphere]].](https://commons.wikimedia.org/wiki/Special:FilePath/F orbital.png?width=200 "The [[atomic orbital]]s of [[chemistry]] are partially described by [[spherical harmonic]]s, which can be used to produce Fourier series on the [[sphere]].")
![The first four partial sums of the Fourier series for a [[square wave]]. As more harmonics are added, the partial sums ''converge to'' (become more and more like) the square wave.](https://commons.wikimedia.org/wiki/Special:FilePath/Fourier Series.svg?width=200 "The first four partial sums of the Fourier series for a [[square wave]]. As more harmonics are added, the partial sums ''converge to'' (become more and more like) the square wave.")
![Four partial sums (Fourier series) of lengths 1, 2, 3, and 4 terms, showing how the approximation to a square wave improves as the number of terms increases [{{filepath:Fourier_series_square_wave_circle_animation.svg}} (animation)]](https://commons.wikimedia.org/wiki/Special:FilePath/Fourier_series_square_wave_circles_animation.gif?width=200 "Four partial sums (Fourier series) of lengths 1, 2, 3, and 4 terms, showing how the approximation to a square wave improves as the number of terms increases [{{filepath:Fourier_series_square_wave_circle_animation.svg}} (animation)]")
![Four partial sums (Fourier series) of lengths 1, 2, 3, and 4 terms, showing how the approximation to a sawtooth wave improves as the number of terms increases [{{filepath:Fourier_series_sawtooth_wave_circles_animation.svg}} (animation)]](https://commons.wikimedia.org/wiki/Special:FilePath/Fourier_series_sawtooth_wave_circles_animation.gif?width=200 "Four partial sums (Fourier series) of lengths 1, 2, 3, and 4 terms, showing how the approximation to a sawtooth wave improves as the number of terms increases [{{filepath:Fourier_series_sawtooth_wave_circles_animation.svg}} (animation)]")
![Example of convergence to a somewhat arbitrary function. Note the development of the "ringing" ([[Gibbs phenomenon]]) at the transitions to/from the vertical sections.](https://commons.wikimedia.org/wiki/Special:FilePath/Example_of_Fourier_Convergence.gif ?width=200 "Example of convergence to a somewhat arbitrary function. Note the development of the \"ringing\" ([[Gibbs phenomenon]]) at the transitions to/from the vertical sections.")
общая лексика
ряд Фурье
Definition
Wikipedia
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In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer.
The subject of Fourier analysis encompasses a vast spectrum of mathematics. 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. For example, determining what component frequencies are present in a musical note would involve computing the Fourier transform of a sampled musical note. One could then re-synthesize the same sound by including the frequency components as revealed in the Fourier analysis. In mathematics, the term Fourier analysis often refers to the study of both operations.
The decomposition process itself is called a Fourier transformation. Its output, the Fourier transform, is often given a more specific name, which depends on the domain and other properties of the function being transformed. Moreover, the original concept of Fourier analysis has been extended over time to apply to more and more abstract and general situations, and the general field is often known as harmonic analysis. Each transform used for analysis (see list of Fourier-related transforms) has a corresponding inverse transform that can be used for synthesis.
To use Fourier analysis, data must be equally spaced. Different approaches have been developed for analyzing unequally spaced data, notably the least-squares spectral analysis (LSSA) methods that use a least squares fit of sinusoids to data samples, similar to Fourier analysis. Fourier analysis, the most used spectral method in science, generally boosts long-periodic noise in long gapped records; LSSA mitigates such problems.
