Dirac delta function

related topics
{math, number, function}
{math, energy, light}
{game, team, player}
{car, race, vehicle}
{style, bgcolor, rowspan}

The Dirac delta function, or δ function, is (informally) a generalized function depending on a real parameter such that it is zero for all values of the parameter except when the parameter is zero, and its integral over the parameter from −∞ to ∞ is equal to one.[1][2] It was introduced by theoretical physicist Paul Dirac. In the context of signal processing it is often referred to as the unit impulse function. It is a continuous analog of the Kronecker delta function which is usually defined on a finite domain, and takes values 0 and 1.

From a purely mathematical viewpoint, the Dirac delta is not strictly a function, because any real function that is equal to zero everywhere but a single point must have total integral zero.[3] While for many purposes the Dirac delta can be manipulated as a function, formally it can be defined as a distribution that is also a measure. In many applications, the Dirac delta is regarded as a kind of limit (a weak limit) of a sequence of functions having a tall spike at the origin. The approximating functions of the sequence are thus "approximate" or "nascent" delta functions.


Full article ▸

related documents
Metric space
Hausdorff dimension
Taylor's theorem
Extended Euclidean algorithm
Uniform continuity
Template (programming)
Set (mathematics)
Cholesky decomposition
Square root
Exponential function
Icon (programming language)
Kernel (matrix)
Tail recursion
Vigenère cipher
Semidirect product
Cantor's diagonal argument
Riemannian manifold
Equivalence relation
Communication complexity
Standard ML
Complete metric space
Category theory
L'Hôpital's rule
Insertion sort