mathematical analysis, the Dirac delta function (or δ distribution), also known as the unit impulse, is a generalized function on the real numbers, whose...
96 KB (14,230 words) - 04:36, 14 May 2025
}\delta (t-kT)} for some given period T {\displaystyle T} . Here t is a real variable and the sum extends over all integers k. The Dirac delta function...
21 KB (3,470 words) - 18:24, 27 January 2025
continuous-time systems the Dirac delta function is often confused for both the Kronecker delta function and the unit sample function. The Dirac delta is defined as:...
19 KB (3,665 words) - 21:39, 15 June 2025
of formalizing the idea of the Dirac delta function, an important tool in physics and other technical fields. A Dirac measure is a measure δx on a set...
6 KB (640 words) - 04:31, 19 December 2022
quantum mechanics the delta potential is a potential well mathematically described by the Dirac delta function - a generalized function. Qualitatively, it...
17 KB (2,721 words) - 07:49, 24 April 2025
Impulse response (redirect from Impulse response function)
function contains all frequencies (see the Fourier transform of the Dirac delta function, showing infinite frequency bandwidth that the Dirac delta function...
10 KB (1,211 words) - 21:36, 25 May 2025
as points with non-zero charge). The Dirac delta function, or δ function, is (informally) a generalized function on the real number line that is zero...
15 KB (1,649 words) - 10:02, 16 May 2025
Green's function G {\displaystyle G} is the solution of the equation L G = δ {\displaystyle LG=\delta } , where δ {\displaystyle \delta } is Dirac's delta function;...
43 KB (5,810 words) - 23:26, 15 June 2025
integral of the Dirac delta function. This is sometimes written as H ( x ) := ∫ − ∞ x δ ( s ) d s {\displaystyle H(x):=\int _{-\infty }^{x}\delta (s)\,ds} although...
14 KB (2,157 words) - 11:06, 13 June 2025
{\displaystyle \delta (t)} is δ ( f ) = 1 , {\displaystyle \delta (f)=1,} means that the frequency spectrum of the Dirac delta function is infinitely broad...
10 KB (1,625 words) - 21:11, 28 May 2025
Laplacian of the indicator (redirect from Surface delta function)
on the indicator function of some domain D. It is a generalisation of the derivative (or "prime function") of the Dirac delta function to higher dimensions;...
30 KB (4,273 words) - 02:42, 21 February 2025
1920s and 1930s further basic steps were taken. The Dirac delta function was boldly defined by Paul Dirac (an aspect of his scientific formalism); this was...
18 KB (2,203 words) - 16:23, 27 December 2024
Infinitesimal (section Infinitesimal delta functions)
continuity in his Cours d'Analyse, and in defining an early form of a Dirac delta function. As Cantor and Dedekind were developing more abstract versions of...
37 KB (5,092 words) - 16:24, 23 May 2025
three-dimensional space, and δ {\displaystyle \delta } is the Dirac delta function. The algebraic expression of the Green's function for the three-variable Laplace operator...
11 KB (1,910 words) - 01:17, 15 August 2024
The Kronecker delta in mathematics. The central difference for a function. The degree of a vertex in graph theory. The Dirac delta function in mathematics...
14 KB (1,611 words) - 15:22, 25 May 2025
distribution becomes a one-point degenerate distribution with a Dirac delta function spike at the right end, x = 1, with probability 1, and zero probability...
245 KB (40,562 words) - 12:56, 14 May 2025
Normal distribution (redirect from Normal density function)
variance as a generalized function; specifically, as a Dirac delta function δ {\displaystyle \delta } translated by the mean μ {\displaystyle \mu }...
151 KB (22,720 words) - 14:33, 14 June 2025
potentials that are not functions but are distributions, such as the Dirac delta function. It is easy to visualize a sequence of functions meeting the requirement...
99 KB (13,587 words) - 21:25, 14 May 2025
career, Dirac made numerous important contributions to mathematical subjects, including the Dirac delta function, Dirac algebra and the Dirac operator...
92 KB (9,987 words) - 20:37, 2 June 2025
the step response to a step input, or the impulse response to a Dirac delta function input. In the frequency domain (for example, looking at the Fourier...
19 KB (2,912 words) - 11:25, 6 June 2025
A Dirac delta function or simply delta function is a generalized function on the real number line denoted by δ that is zero everywhere except at zero...
813 bytes (150 words) - 03:41, 17 December 2022
arguments. The integral of the Dirac delta function. Sawtooth wave Square wave Triangle wave Rectangular function Floor function: Largest integer less than...
10 KB (1,065 words) - 21:59, 6 March 2025
estimated wavelet to a Dirac delta function (i.e., a spike). The result may be seen as a series of scaled, shifted delta functions (although this is not...
16 KB (1,975 words) - 01:58, 14 January 2025
distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields Medal in 1950 for his work on the theory...
17 KB (2,004 words) - 04:38, 1 January 2025
functions. Symmetric function: value is independent of the order of its arguments Generalized function: a wide generalization of Dirac delta function...
13 KB (1,407 words) - 00:18, 19 May 2025
approaches zero, the right-hand side approaches δ(x − 1), where δ is the Dirac delta function. This admits the limit (in the distributional sense): ∫ 0 ∞ k J α...
76 KB (12,308 words) - 06:31, 12 June 2025
relatively simple applications use the Dirac delta function, which can be treated formally as if it were a function, but the justification requires a mathematically...
177 KB (21,313 words) - 02:31, 2 June 2025
step function is equal to the Dirac delta function, i.e. d H ( x ) d x = δ ( x ) {\displaystyle {\frac {\mathrm {d} H(x)}{\mathrm {d} x}}=\delta (x)}...
17 KB (2,543 words) - 13:47, 8 May 2025
Reproducing kernel Hilbert space (redirect from Bergman kernel function)
non-existent Dirac delta function). However, there are RKHSs in which the norm is an L2-norm, such as the space of band-limited functions (see the example...
33 KB (6,325 words) - 05:39, 15 June 2025
provides an exact solution to the quantum-mechanical double-well Dirac delta function model for equal charges—a fundamental problem in physics. Prompted...
78 KB (12,432 words) - 01:04, 6 June 2025