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Fourier Series Illustration
Fourier may refer to: People named Fourier *Joseph Fourier (1768–1830), French mathematician and physicist *Charles Fourier (1772–1837), French utopian socialist thinker *Peter Fourier (1565–1640), French saint in the Roman Catholic Church and priest of Mattaincourt Mathematics *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 *Fourier operator, the kernel of the Fredholm integral of the first kind that defines the continuous Fourier transform * Fourier inversion theorem, any one of several theorems by which Fourier inversion recovers a function from its Fourier transform *Short-time Fourier transform or short-term Fourier transform (STFT), a Fourier transform during a short term of time, used in the area of signal analysis * Frac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Fourier
Jean-Baptiste Joseph Fourier (; ; 21 March 1768 – 16 May 1830) was a French people, 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. The Fourier transform and Thermal conduction#Fourier.27s law, Fourier's law of conduction are also named in his honour. Fourier is also generally credited with the discovery of the greenhouse effect. Biography Fourier was born at Auxerre (now in the Yonne département of France), the son of a tailor. He was orphaned at the age of nine. Fourier was recommended to the Bishop of Auxerre and, through this introduction, he was educated by the Benedictine Order of the Convent of St. Mark. The commissions in the scientific corps of the army were reserved for those of good birth, and being thus ineligible, he accepted a military lectureship on mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Fourier Transform
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies. It has the same sample-values as the original input sequence. The DFT is therefore said to be a frequency domain representation of the original input sequence. If the original sequence spans all the non-zero values of a function, its DTFT is continuous (and periodic), and the DFT provides discrete samples of one cycle. If the original sequence is one cycle of a periodic function, the DFT provides all the non-zero values of one DTFT cycle. The DFT is the most important discret ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French-language Surnames
French ( or ) is a Romance language of the Indo-European family. It descended from the Vulgar Latin of the Roman Empire, as did all Romance languages. French evolved from Gallo-Romance, the Latin spoken in Gaul, and more specifically in Northern Gaul. Its closest relatives are the other langues d'oïl—languages historically spoken in northern France and in southern Belgium, which French (Francien) largely supplanted. French was also influenced by native Celtic languages of Northern Roman Gaul like Gallia Belgica and by the ( Germanic) Frankish language of the post-Roman Frankish invaders. Today, owing to France's past overseas expansion, there are numerous French-based creole languages, most notably Haitian Creole. A French-speaking person or nation may be referred to as Francophone in both English and French. French is an official language in 29 countries across multiple continents, most of which are members of the ''Organisation internationale de la Francophonie'' (OI ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Occupational Surnames
In some cultures, a surname, family name, or last name is the portion of one's personal name that indicates one's family, tribe or community. Practices vary by culture. The family name may be placed at either the start of a person's full name, as the forename, or at the end; the number of surnames given to an individual also varies. As the surname indicates genetic inheritance, all members of a family unit may have identical surnames or there may be variations; for example, a woman might marry and have a child, but later remarry and have another child by a different father, and as such both children could have different surnames. It is common to see two or more words in a surname, such as in compound surnames. Compound surnames can be composed of separate names, such as in traditional Spanish culture, they can be hyphenated together, or may contain prefixes. Using names has been documented in even the oldest historical records. Examples of surnames are documented in the 11th ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier (crater)
Fourier is a lunar impact crater that is located in the southwestern part of the Moon's near side, just to the southeast of the crater Vieta. To the northeast is the Mare Humorum. The rim of this crater is roughly circular, but appears oval when viewed from the Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ... due to foreshortening. Except to the north-northwest, the outer rim is not heavily eroded. The satellite crater Fourier B lies along the eastern rim and inner side. The inner wall is relatively wide, and is slumped slightly along the edge forming a shelf near the perimeter. The interior floor is just over half the diameter of the crater rim, and is relatively level with a small crater to the west of the midpoint and another near the northeast edge. Satellite craters B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Fourier-related Transforms
This is a list of linear transformations of function (mathematics), functions related to Fourier analysis. Such transformations Map (mathematics), map a function to a set of coefficients of basis functions, where the basis functions are trigonometric function, sinusoidal and are therefore strongly localized in the frequency spectrum. (These transforms are generally designed to be invertible.) In the case of the Fourier transform, each basis function corresponds to a single frequency component. Continuous transforms Applied to functions of continuous arguments, Fourier-related transforms include: * Two-sided Laplace transform * Mellin transform, another closely related integral transform * Laplace transform * Fourier transform, with special cases: ** Fourier series *** When the input function/waveform is periodic, the Fourier transform output is a Dirac comb function, modulated by a discrete sequence of finite-valued coefficients that are complex-valued in general. These are cal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform Spectroscopy
Fourier-transform spectroscopy is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source, using time-domain or space-domain measurements of the radiation, electromagnetic or not. It can be applied to a variety of types of ''spectroscopy'' including optical spectroscopy, infrared spectroscopy ( FTIR, FT-NIRS), nuclear magnetic resonance (NMR) and magnetic resonance spectroscopic imaging (MRSI), mass spectrometry and electron spin resonance spectroscopy. There are several methods for measuring the temporal coherence of the light (see: field-autocorrelation), including the continuous-wave and the pulsed Fourier-transform spectrometer or Fourier-transform spectrograph. The term "Fourier-transform spectroscopy" reflects the fact that in all these techniques, a Fourier transform is required to turn the raw data into the actual spectrum, and in many of the cases in optics involving interferometers, is based on the Wiener– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Fourier Series
In mathematical analysis, many generalizations of Fourier series have proved to be useful. They are all special cases of decompositions over an orthonormal basis of an inner product space. Here we consider that of square-integrable functions defined on an interval of the real line, which is important, among others, for interpolation theory. Definition Consider a set of square-integrable functions with values in \mathbb = \Complex or \mathbb = \R, \Phi = \_^\infty, which are pairwise orthogonal for the inner product \langle f, g\rangle_w = \int_a^b f(x)\,\overline(x)\,w(x)\,dx where w(x) is a weight function, and \overline\cdot represents complex conjugation, i.e., \overline(x) = g(x) for \mathbb = \R. The generalized Fourier series of a square-integrable function f : , b\to \mathbb, with respect to Φ, is then f(x) \sim \sum_^\infty c_n\varphi_n(x), where the coefficients are given by c_n = . If Φ is a complete set, i.e., an orthogonal basis of the space of all square-in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fast Fourier Transform
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical. An FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors. As a result, it manages to reduce the complexity of computing the DFT from O\left(N^2\right), which arises if one simply applies the definition of DFT, to O(N \log N), where N is the data size. The difference in speed can be enormous, especially for long data sets where ''N'' may be in the thousands or millions. In the presence of round-off error, many FFT algorithm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete-time Fourier Transform
In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of values. The DTFT is often used to analyze samples of a continuous function. The term ''discrete-time'' refers to the fact that the transform operates on discrete data, often samples whose interval has units of time. From uniformly spaced samples it produces a function of frequency that is a periodic summation of the continuous Fourier transform of the original continuous function. Under certain theoretical conditions, described by the sampling theorem, the original continuous function can be recovered perfectly from the DTFT and thus from the original discrete samples. The DTFT itself is a continuous function of frequency, but discrete samples of it can be readily calculated via the discrete Fourier transform (DFT) (see ), which is by far the most common method of modern Fourier analysis. Both transforms are invertible. The inverse DTFT is the origin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Fourier
François Marie Charles Fourier (;; 7 April 1772 – 10 October 1837) was a French philosopher, an influential early socialist thinker and one of the founders of utopian socialism. Some of Fourier's social and moral views, held to be radical in his lifetime, have become mainstream thinking in modern society. For instance, Fourier is credited with having originated the word ''feminism'' in 1837. Fourier's social views and proposals inspired a whole movement of intentional communities. Among them in the United States were the community of Utopia, Ohio; La Reunion near present-day Dallas, Texas; Lake Zurich, Illinois; the North American Phalanx in Red Bank, New Jersey; Brook Farm in West Roxbury, Massachusetts; the Community Place and Sodus Bay Phalanx in New York State; Silkville, Kansas, and several others. In Guise, France, he influenced the . Fourier later inspired a diverse array of revolutionary thinkers and writers. Life Fourier was born in Besançon, France on 7 April 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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