simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing...
37 KB (4,735 words) - 14:55, 8 September 2024
In physics, engineering and mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function...
177 KB (21,024 words) - 16:44, 12 September 2024
is generally called Fourier analysis, although the term is sometimes used interchangeably with harmonic analysis. Harmonic analysis has become a vast subject...
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A Fourier series (/ˈfʊrieɪ, -iər/) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a...
70 KB (10,863 words) - 12:21, 11 September 2024
In Fourier analysis, a multiplier operator is a type of linear operator, or transformation of functions. These operators act on a function by altering...
25 KB (2,815 words) - 11:04, 15 September 2021
fast Fourier transform (FFT) is an algorithm that computes the Discrete Fourier Transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts...
63 KB (7,383 words) - 11:48, 9 September 2024
Hilbert space (redirect from Hilbert spaces and Fourier analysis)
the theories of partial differential equations, quantum mechanics, Fourier analysis (which includes applications to signal processing and heat transfer)...
128 KB (17,487 words) - 22:34, 20 June 2024
of Fourier analysis topics. See also the list of Fourier-related transforms, and the list of harmonic analysis topics. Multiplier (Fourier analysis) Fourier...
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initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems...
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Fourier-transform infrared spectroscopy (FTIR) is a technique used to obtain an infrared spectrum of absorption or emission of a solid, liquid, or gas...
37 KB (4,774 words) - 17:15, 5 September 2024
The short-time Fourier transform (STFT) is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections...
22 KB (4,051 words) - 16:46, 1 August 2024
physics and harmonic analysis, the quadratic Fourier transform is an integral transform that generalizes the fractional Fourier transform, which in turn...
2 KB (177 words) - 18:40, 3 December 2023
This is a list of harmonic analysis topics. See also list of Fourier analysis topics and list of Fourier-related transforms, which are more directed towards...
3 KB (202 words) - 12:10, 30 October 2023
In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of discrete values. The DTFT...
40 KB (5,163 words) - 00:26, 21 June 2024
The DFT is the most important discrete transform, used to perform Fourier analysis in many practical applications. In digital signal processing, the function...
72 KB (11,236 words) - 07:45, 27 August 2024
analysis are extended to the analysis of electroencephalography (EEG). These include wavelet analysis and Fourier analysis, with new focus on shared activity...
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order, Fourier Analysis: An Introduction; Complex Analysis; Real Analysis: Measure Theory, Integration, and Hilbert Spaces; and Functional Analysis: Introduction...
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the result of Fourier analysis of a periodic function Fourier analysis, the description of functions as sums of sinusoids Fourier transform, the type of...
2 KB (363 words) - 07:36, 2 June 2024
Fourier-transform spectroscopy is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source,...
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In numerical analysis, von Neumann stability analysis (also known as Fourier stability analysis) is a procedure used to check the stability of finite difference...
10 KB (1,415 words) - 01:49, 20 August 2024
This is a list of linear transformations of functions related to Fourier analysis. Such transformations map a function to a set of coefficients of basis...
7 KB (1,002 words) - 19:07, 10 September 2024
computing, the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. The...
20 KB (3,299 words) - 10:26, 12 September 2024
Sine wave (section Fourier analysis)
monochromatic radiation. In engineering, signal processing, and mathematics, Fourier analysis decomposes general functions into a sum of sine waves of various frequencies...
10 KB (1,332 words) - 06:12, 25 March 2024
mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform. Intuitively...
18 KB (3,626 words) - 17:26, 23 July 2024
Laplace transform (redirect from Fourier–Laplace transform)
moments. Also unlike the Fourier transform, when regarded in this way as an analytic function, the techniques of complex analysis, and especially contour...
75 KB (9,390 words) - 06:38, 28 August 2024
analysis (LSSA) is a method of estimating a frequency spectrum based on a least-squares fit of sinusoids to data samples, similar to Fourier analysis...
28 KB (3,354 words) - 11:45, 30 May 2024
Basis function (redirect from Fourier basis)
in an inner-product space Orthogonal polynomials Fourier analysis and Fourier series Harmonic analysis Orthogonal wavelet Biorthogonal wavelet Radial basis...
3 KB (336 words) - 02:35, 22 July 2022
Fourier profilometry is a method for measuring profiles using distortions in periodic patterns. The method uses Fourier analysis (a 2-dimensional fast...
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field of calculus and Fourier analysis, the Fourier sine and cosine series are two mathematical series named after Joseph Fourier. In this article, f denotes...
2 KB (364 words) - 19:51, 16 January 2023
18th century, into analysis topics such as the calculus of variations, ordinary and partial differential equations, Fourier analysis, and generating functions...
45 KB (4,351 words) - 09:12, 27 August 2024