Signal magnitude area

In mathematics, the signal magnitude area (abbreviated SMA or sma) is a statistical measure of the magnitude of a varying quantity.

Definition
The SMA value of a set of values (or a continuous-time waveform) is the normalized integral of the original values.

In the case of a set of n values $$\{x_1,x_2,\dots,x_n\}$$ matching a time length T, the SMA



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:



f_\text{sma}= {1 \over T} \int_0^T |x(t)-a_x|+|y(t)-a_y|+|z(t)-a_z| \, dt $$