The Dirac delta function, often written as formula_1, is a made-up concept by mathematician Paul Dirac. It is a really pointy and skinny function that pokes out a point along a wave. Loosely speaking, it has the value of zero everywhere except at formula_2, in such a way that the area between the function and the "x"-axis adds up to 1. The delta function is often used in sampling theory, where its pointiness is useful for getting clean samples.