(1)	$\begin{array}{l}\displaystyle < A>_w \, = \frac{ \int_{t_0}^t A(t) \, \mathrm{w}(t) \, dt }{\int_0^{t_0} \, \mathrm{w}(t) \, dt }\end{array}$

where

$\begin{array}{l}t\end{array}$	time-line
$\begin{array}{l}t_0\end{array}$	initial time
$\begin{array}{l}A(t)\end{array}$	time-based variable
$\begin{array}{l}\mathrm{w}(t)\end{array}$	weighting function

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See also