DefinitionThe Dirac delta function from the family of all delta functions δ, is a generalized function on the real number line. It is defined by the property However, more precisely, the Dirac delta is the measure corresponding to this generalized function. The name refers to the mathematician Paul A.M. Dirac, who proposed the function in the 1930s. In the half-century that has passed, the delta function has rudely entered into various branches of science. Especially it likeut physicists, engineers and signal processing engineers, because they have a very common, if not more correct mathematically, device, namely the delta Dirac function, to describe impulsive or concentrated effects; for example, he describes point masses, point charges, etc. On this basis, this function is still being used in the theory of distributions, where pointwise estimation is not necessary. The delta function δ x { \displaystyle \delta x} satisfies the property and, for all functions f x { \displaystyle f(x)} , that are continuous on the whole real line:
