Signal magnitude area
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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 [math]\displaystyle{ \{x_1,x_2,\dots,x_n\} }[/math] matching a time length T, the SMA
- [math]\displaystyle{ x_\text{sma} = \sum_{i=1}^n x_i }[/math]
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]
- [math]\displaystyle{ f_\text{sma}= {1 \over T} \int_0^T |x(t)-a_x|+|y(t)-a_y|+|z(t)-a_z| \, dt }[/math]
See also
References
- ↑ "Matlab compute Normalized Signal Magnitude area". https://stackoverflow.com/questions/19702753/matlab-compute-normalized-signal-magnitude-area.
- ↑ 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.
- ↑ "Classifying prosthetic use via accelerometry in persons with transtibial amputations". U.S. Department of Veteran Affairs. 2013. http://www.rehab.research.va.gov/jour/2013/509/jrrd-2012-12-0233.html. Retrieved 2014-10-14.
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