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 (21,044 words) - 13:14, 5 August 2024
A fast Fourier transform (FFT) is an algorithm that computes the Discrete Fourier Transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis...
63 KB (7,365 words) - 21:28, 19 August 2024
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of...
71 KB (11,045 words) - 03:18, 22 July 2024
the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. The quantum...
20 KB (3,245 words) - 06:47, 28 July 2024
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) - 15:30, 26 June 2024
The decomposition process itself is called a Fourier transformation. Its output, the Fourier transform, is often given a more specific name, which depends...
37 KB (4,733 words) - 18:28, 14 May 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
Fourier-transform spectroscopy is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source,...
15 KB (1,888 words) - 17:19, 20 March 2023
fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to...
25 KB (3,736 words) - 13:47, 1 August 2024
other transforms, most notably the Fourier transform and the Mellin transform. Formally, the Laplace transform is converted into a Fourier transform by the...
75 KB (9,294 words) - 00:53, 3 August 2024
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
classical Fourier transform, the eigenvalues represent frequencies and eigenvectors form what is known as a graph Fourier basis. The Graph Fourier transform is...
12 KB (1,845 words) - 15:56, 26 June 2024
The Fourier transform is also part of Fourier analysis, but is defined for functions on R n {\displaystyle \mathbb {R} ^{n}} . Since Fourier's time,...
68 KB (10,430 words) - 12:34, 1 August 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
arguments, Fourier-related transforms include: Two-sided Laplace transform Mellin transform, another closely related integral transform Laplace transform Fourier...
7 KB (933 words) - 23:28, 7 November 2023
Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an...
32 KB (4,709 words) - 01:37, 14 July 2024
is also known as the Fourier–Bessel transform. Just as the Fourier transform for an infinite interval is related to the Fourier series over a finite interval...
26 KB (4,204 words) - 00:07, 22 July 2024
In mathematics, the discrete Fourier transform over a ring generalizes the discrete Fourier transform (DFT), of a function whose values are commonly complex...
19 KB (3,807 words) - 02:04, 6 August 2024
the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups. The Fourier transform...
12 KB (1,855 words) - 19:56, 29 July 2024
In mathematics, the Fourier sine and cosine transforms are forms of the Fourier transform that do not use complex numbers or require negative frequency...
7 KB (1,196 words) - 01:37, 24 October 2023
Laplace transform (the s-domain or s-plane). This similarity is explored in the theory of time-scale calculus. While the continuous-time Fourier transform is...
38 KB (4,621 words) - 11:36, 3 June 2024
In mathematics the finite Fourier transform may refer to either another name for discrete-time Fourier transform (DTFT) of a finite-length series. E.g...
2 KB (298 words) - 14:04, 23 July 2023
heat transfer and vibrations. The Fourier transform and Fourier's law of conduction are also named in his honour. Fourier is also generally credited with...
24 KB (2,296 words) - 05:37, 15 July 2024
the sign of the frequency (see § Relationship with the Fourier transform). The Hilbert transform is important in signal processing, where it is a component...
59 KB (8,095 words) - 17:59, 8 August 2024
Fourier-transform ion cyclotron resonance mass spectrometry is a type of mass analyzer (or mass spectrometer) for determining the mass-to-charge ratio...
17 KB (2,196 words) - 18:39, 25 March 2024
quadratic Fourier transform is an integral transform that generalizes the fractional Fourier transform, which in turn generalizes the Fourier transform. Roughly...
2 KB (177 words) - 18:40, 3 December 2023
formula for the inverse Laplace transform, called the Mellin's inverse formula, the Bromwich integral, or the Fourier–Mellin integral, is given by the...
8 KB (1,004 words) - 09:51, 20 January 2024
Harmonic analysis (redirect from Fourier theory)
by using the Fourier transform for functions on the real line or by Fourier series for periodic functions. Generalizing these transforms to other domains...
13 KB (1,566 words) - 19:54, 17 August 2024
discrete Fourier transform (NUDFT or NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier transform or discrete-time Fourier transform...
14 KB (2,447 words) - 19:10, 12 August 2024
The Radon transform is closely related to the Fourier transform. We define the univariate Fourier transform here as: f ^ ( ω ) = ∫ − ∞ ∞ f ( x ) e − 2 π...
24 KB (3,492 words) - 18:00, 23 June 2024