title: Signal magnitude area
text: # 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:
  
      $f_{\text{sma}}={1 \over T}\int _{0}^{T}|x(t)-a_{x}|+|y(t)-a_{y}|+|z(t)-a_{z}|\,dt$
  