Dirac Delta Function

The Dirac delta or Dirac's delta is a mathematical construct introduced by the British theoretical physicist Paul Dirac. Informally, it is a function representing an infinitely sharp peak bounding unit area: a function δ(x) that has the value zero everywhere except at x = 0 where its value is infinitely large in such a way that its total integral is 1. It is a continuous analogue of the discrete Kronecker delta. In the context of signal processing it is often referred to as the unit impulse function. Note that the Dirac delta is not strictly a function. While for many purposes it can be manipulated as such, formally it can be defined as a distribution that is also a measure.

Plot of the Dirac delta function. Schematic representation of the Dirac delta function for x₀ = 0. A line surmounted by an arrow is usually used to schematically represent the Dirac delta function. The height of the arrow is usually used to specify the value of any multiplicative constant, which will give the area under the function. The other convention is to write the area next to the arrowhead.

http://en.wikipedia.org/wiki/Dirac_delta_function