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. ^{[1] [2]}

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:^[3]

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

See also

• Root mean square

References

1. "Matlab compute Normalized Signal Magnitude area".
2. "Frequency domain approach for activity classification using accelerometer, section 3B. Detection Algorithm".
3. "Classifying prosthetic use via accelerometry in persons with transtibial amputations". Journal of Rehabilitation Research & Development. U.S. Department of Veteran Affairs. 2013. Retrieved 2014-10-14.