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
simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing...
37 KB (4,734 words) - 13:29, 14 September 2024
In mathematics, the question of whether the Fourier series of a periodic function converges to a given function is researched by a field known as classical...
22 KB (4,043 words) - 09:31, 28 August 2024
In mathematics, Fourier–Bessel series is a particular kind of generalized Fourier series (an infinite series expansion on a finite interval) based on Bessel...
15 KB (2,344 words) - 13:59, 4 October 2024
Discrete Fourier transform *DFT matrix Fast Fourier transform Fourier integral operator Fourier inversion theorem Fourier multiplier Fourier series Fourier sine...
177 KB (20,975 words) - 10:11, 15 October 2024
certain sense one could say that the Taylor series is "local" and the Fourier series is "global". The Taylor series is defined for a function which has infinitely...
48 KB (8,253 words) - 23:24, 11 October 2024
In digital signal processing, a discrete Fourier series (DFS) is a Fourier series whose sinusoidal components are functions of discrete time instead of...
4 KB (610 words) - 16:18, 16 August 2024
best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications...
24 KB (2,296 words) - 08:58, 13 September 2024
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) - 18:07, 9 October 2024
generalized Fourier series is the expansion of a square integrable function into a sum of square integrable orthogonal basis functions. The standard Fourier series...
9 KB (1,582 words) - 07:54, 10 September 2024
Dirichlet series ∑ n = 1 ∞ a n n s . {\textstyle \sum _{n=1}^{\infty }{\frac {a_{n}}{n^{s}}}.} Used in number theory.[citation needed] A Fourier series is an...
9 KB (972 words) - 16:29, 11 October 2024
Fourier may refer to: Fourier (surname), French surname Fourier series, a weighted sum of sinusoids having a common period, the result of Fourier analysis...
2 KB (363 words) - 07:36, 2 June 2024
Harmonic analysis (redirect from Fourier theory)
representation is found by using the Fourier transform for functions on unbounded domains such as the full real line or by Fourier series for functions on bounded...
14 KB (1,634 words) - 20:00, 15 October 2024
Heat equation (redirect from Solving the heat equation using Fourier series)
functions. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses...
58 KB (9,816 words) - 10:11, 12 September 2024
Dirichlet–Jordan test (redirect from Dirichlet Fourier series conditions)
f to be equal to the sum of its Fourier series at a point of continuity. Moreover, the behavior of the Fourier series at points of discontinuity is determined...
7 KB (964 words) - 16:22, 15 October 2024
Dirac comb (section Fourier series)
Because the Dirac comb function is periodic, it can be represented as a Fourier series based on the Dirichlet kernel: Ш T ( t ) = 1 T ∑ n = − ∞ ∞ e i 2...
20 KB (3,462 words) - 09:42, 2 October 2024
infinite version of a trigonometric polynomial. A trigonometric series is called the Fourier series of the integrable function f {\textstyle f} if the coefficients...
5 KB (772 words) - 15:42, 10 October 2024
Hilbert space (redirect from Hilbert spaces and Fourier analysis)
fundamental wave). A significant problem in classical Fourier series asks in what sense the Fourier series converges, if at all, to the function f. Hilbert...
128 KB (17,488 words) - 18:46, 10 October 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 (7,407 words) - 12:49, 14 October 2024
In the mathematical field of Fourier analysis, the conjugate Fourier series arises by realizing the Fourier series formally as the boundary values of...
2 KB (289 words) - 17:51, 28 April 2022
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...
41 KB (5,320 words) - 12:25, 13 October 2024
Real analysis (section Fourier series)
exponentials). The study of Fourier series typically occurs and is handled within the branch mathematics > mathematical analysis > Fourier analysis. Integration...
49 KB (7,673 words) - 10:05, 6 August 2024
specific types of series there are more specialized convergence tests, for instance for Fourier series there is the Dini test. A series of real- or complex-valued...
68 KB (11,199 words) - 22:51, 16 October 2024
Gibbs phenomenon (category Fourier series)
the Fourier series of a piecewise continuously differentiable periodic function around a jump discontinuity. The N {\textstyle N} th partial Fourier series...
37 KB (5,592 words) - 19:22, 1 October 2024
of the duration of the input sequence. An inverse DFT (IDFT) is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the...
72 KB (11,265 words) - 18:31, 14 October 2024
in general. These are called Fourier series coefficients. The term Fourier series actually refers to the inverse Fourier transform, which is a sum of...
7 KB (1,002 words) - 19:07, 10 September 2024
Uses of trigonometry (section Fourier series)
technical, such as in number theory. The mathematical topics of Fourier series and Fourier transforms rely heavily on knowledge of trigonometric functions...
12 KB (1,646 words) - 00:36, 9 October 2024
the continuous-time Fourier transform is evaluated on the s-domain's vertical axis (the imaginary axis), the discrete-time Fourier transform is evaluated...
38 KB (4,624 words) - 13:33, 13 October 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
fact an element of an infinite-dimensional vector space ℓ2 , and thus Fourier series is a linear operator. When dealing with general function R → C {\displaystyle...
13 KB (1,857 words) - 21:52, 8 May 2024