| distribution, defined as the limit of a positive function, equal to zero outside a small interval containing the origin, the integral of which remains equal to one when this interval tends to zero|
SEE: Figure 4a) and IEC 60027-6.
Note 1 to entry: A distribution assigns a number to any function f(t), sufficiently smooth for t = t0 [see CEI 60050-103:2009, 103-03-05].
The Dirac impulse does this according to
Note 2 to entry: Any shape with area 1 may be used for the definition of δ(t), e.g. a rectangular pulse with width τ and height τ–1, or a triangular pulse, as shown in Figure 4a), as well as a Gaussian function
Note 3 to entry: Any of the shapes mentioned in Note 2 to entry with τ much smaller than the smallest time constant at work in the system under consideration may be used for a technical approximation of the Dirac impulse.
Note 4 to entry: In control technology the Dirac function is mainly important for the definition of impulses and exclusively used as a function of time. Therefore the term Dirac impulse is used and the definition is adapted accordingly.