IEVref: | 351-45-29 | ID: | |

Language: | en | Status: Standard | |

Term: | unit-impulse response | ||

Synonym1: | weighting function [Preferred] | ||

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Symbol: | g(t)
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Definition: | quotient impulse response Δv_{δ}(t) divided by the impulse area K_{δ} of the impulse function, the quotient described by$g\left(t\right)=\frac{1}{{K}_{\text{\delta}}}\cdot \Delta {v}_{\delta}\left(t\right)$ Note 1 to entry: The unit-impulse response $\Delta v\left(t\right)={\displaystyle \underset{-\infty}{\overset{\infty}{\int}}g\left(\tau \right)}\cdot \Delta u\left(t-\tau \right)\text{d}\tau $. Note 2 to entry: The systems frequency response $G\left(\text{j}\cdot \omega \right)$ may be calculated by Fourier transformation of $G\left(\text{j}\cdot \omega \right)=\mathcal{F}\left\{g\left(t\right)\right\}$. Note 3 to entry: The unit-impulse response of a system mathematically may be considered to result from application of a unit impulse to an input variable. Note 4 to entry: This entry was numbered 351-24-19 in IEC 60050-351:2006. | ||

Publication date: | 2013-11 | ||

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$g\left(t\right)=\frac{1}{{K}_{\text{\delta}}}\cdot \Delta {v}_{\delta}\left(t\right)$

Note 1 to entry: The unit-impulse response *g*(*t*) of a system contains all properties of the system and is used to calculate the response Δ*v*(*t*) of the system to any input variable Δ*u*(*t*) by the convolution integral

$\Delta v\left(t\right)={\displaystyle \underset{-\infty}{\overset{\infty}{\int}}g\left(\tau \right)}\cdot \Delta u\left(t-\tau \right)\text{d}\tau $.

Note 2 to entry: The systems frequency response $G\left(\text{j}\cdot \omega \right)$ may be calculated by Fourier transformation of *g*(*t*):

$G\left(\text{j}\cdot \omega \right)=\mathcal{F}\left\{g\left(t\right)\right\}$.

Note 3 to entry: The unit-impulse response of a system mathematically may be considered to result from application of a unit impulse to an input variable.

Note 4 to entry: This entry was numbered 351-24-19 in IEC 60050-351:2006.