Diraq Delta

This equation represents the Diraq Delta function which is zero everywhere except at x = 0, where x is infinity.

NOTES

The Dirac delta function is a function on the real number line whose value is zero for all real numbers, except for zero.  At zero, the function's value is infinite.  The Diraq Delta function is notionally represented as an infinitely high and infinitely thin spike at the origin.  At the same time the  total area under the spike is exactly one. 

The concept was introduced by Paul Dirac, a theoretical physicist and is closely related to the Kronecker delta function which is similarly 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 extended-real function that is equal to zero everywhere but a single point must have total integral zero.

EXAMPLES

This function represents the density of an idealized point mass and is often used in the signal processing representing the unit impulse.