Signal magnitude area

The SMA value of a set of values (or a continuous-time waveform) is the normalized integral of the original values. ^[1][2]

In the case of a set of n values ${\displaystyle \{x_{1},x_{2},\dots ,x_{n}\}}$ matching a time length T, the SMA

${\displaystyle x_{\text{sma}}=\sum _{i=1}^{n}x_{i}}$

In the continuous domain, we have for example, with a 3-axis signal with an offset correction a for each axis, the following equation:^[3]

${\displaystyle f_{\text{sma}}={1 \over T}\int _{0}^{T}|x(t)-a_{x}|+|y(t)-a_{y}|+|z(t)-a_{z}|\,dt}$

• Root mean square