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

↑ "Matlab compute Normalized Signal Magnitude area".
↑ "Frequency domain approach for activity classification using accelerometer, section 3B. Detection Algorithm".
↑ "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.

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