Editing Moving average (section)

== Continuous moving average ==
The continuous moving average is defined with the following integral. The <math>\varepsilon</math> environment <math> [ x_o-\varepsilon, x_o+\varepsilon] </math> around <math>x_o</math> defines the intensity of smoothing of the graph of the function.
:<math>
 \begin{array}{rrcl} 
   f: & \mathbb{R}   & \rightarrow & \mathbb{R} \\ 
       &   x  & \mapsto & f\left( x \right) 
  \end{array} 
</math>
The continuous moving average of the function <math>f</math> is defined as:
:<math>
 \begin{array}{rrcl} 
   MA_f: & \mathbb{R}   & \rightarrow & \mathbb{R} \\ 
       &   x  & \mapsto & \displaystyle \frac{1}{2\cdot \varepsilon} \cdot \int_{x_o -\varepsilon}^{x_o +\varepsilon} f\left( t \right) \, dt 
  \end{array} 
 </math>
A larger <math> \varepsilon > 0 </math> smoothes the source graph of the function (blue) <math>f</math> more. The animations below show the moving average as animation in dependency of different values for  <math> \varepsilon > 0 </math>. The fraction <math>\frac{1}{2\cdot \varepsilon} </math> is used, because <math> 2\cdot \varepsilon </math> is the interval width for the integral.

<gallery widths=240>
File:Moving average sin polynom mov av.gif|Continuous moving average sine and polynom - visualization of the smoothing with a small interval for integration
File:Moving average sine and polynom with a larger interval.gif|Continuous moving average sine and polynom - visualization of the smoothing with a larger interval for integration
File:Moving average sine and polynom - visualization of interval width.gif|Animation showing the impact of interval width and smoothing by moving average.
</gallery>