• Thumbnail for Dirac delta function
    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
  • Thumbnail for Dirac comb
    }\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
  • Thumbnail for Dirac measure
    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
  • Thumbnail for Impulse response
    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
  • Thumbnail for Point (geometry)
    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
  • Thumbnail for Green's function
    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
  • Thumbnail for Heaviside step function
    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
  • Thumbnail for Rectangular function
    {\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
  • 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
  • Thumbnail for Infinitesimal
    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
  • Thumbnail for Beta distribution
    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
  • Thumbnail for Normal distribution
    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
  • Thumbnail for Wave function
    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
  • Thumbnail for Paul Dirac
    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
  • Thumbnail for Deconvolution
    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
  • Thumbnail for Laurent Schwartz
    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
  • Thumbnail for Bessel function
    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
  • Thumbnail for Fourier transform
    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
  • Thumbnail for Indicator function
    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
  • Thumbnail for Reproducing kernel Hilbert space
    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
  • Thumbnail for Lambert W function
    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