Delta Function

(redirected from Unit impulse function)

delta function

[′del·tə ‚fəŋk·shən]
(mathematics)
A distribution δ such that is ƒ(x). Also known as Dirac delta function; Dirac distribution; unit impulse.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Delta Function

 

(also δ function, Dirac delta function, or δ(x)), a symbol used in mathematical physics in solving problems in which there are point magnitudes (for example, point load and point charge). The delta function can be defined as the density of the distribution of masses, for which a unit mass is concentrated at the point x = 0, while the mass at all other points is equal to zero. Therefore, it is assumed that δ(x) = 0, when x ≠ 0 and δ(0) = ∞, while Delta Function (“infinite splash” of a “unit intensity”). More precisely, the delta function is the name of the generalized function defined by the equality

which is valid for all continuous functions φ(x).

In the theory of generalized functions, the delta function is the name of the functional itself, which is defined by this equality.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.