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Signal magnitude area

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For other uses, see RMS.

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 , … , x n } {\displaystyle \{x_{1},x_{2},\dots ,x_{n}\}} matching a time length T, the SMA

x sma = ∑ i = 1 n x i {\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:

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

See also

References

  1. "Matlab compute Normalized Signal Magnitude area".
  2. Chung, W. Y.; Purwar, A.; Sharma, A. (2008). "Frequency domain approach for activity classification using accelerometer, section 3B. Detection Algorithm". pp. 1120–3. arXiv:1107.4417.
  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.
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