IEVref: 351-45-20 ID: Language: en Status: Standard Term: unit impulse Synonym1: Dirac impulse [Preferred] Synonym2: Synonym3: Symbol: δ(t) Definition: 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$\delta \left(t\right)=\left\{\begin{array}{c}0\\ \infty \\ 0\end{array}\begin{array}{c}\text{\hspace{0.17em}}\text{for}\text{\hspace{0.17em}}t<0\\ \text{\hspace{0.17em}}\text{for}\text{\hspace{0.17em}}t=0\\ \text{\hspace{0.17em}}\text{for}\text{\hspace{0.17em}}t>0\end{array}\text{ }\text{with}\underset{-\infty }{\overset{+\infty }{\int }}\delta \left(t\right)\text{\hspace{0.17em}}\mathrm{d}t=1$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$f\left({t}_{0}\right)=\underset{-\infty }{\overset{\infty }{\int }}\delta \left(t-{t}_{0}\right)f\left(t\right)\text{d}t$.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$\frac{1}{\tau \cdot \sqrt{\pi }}\cdot {e}^{-\text{\hspace{0.17em}}\frac{{t}^{2}}{{\tau }^{2}}}$.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. Publication date: 2013-11 Source: Replaces: Internal notes: 2017-06-02: Cleanup - Remove Attached Image 351-45-201_en.gif CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5: