Median Smoothing

The method is based on moving median calculation. To calculate moving median at the point t, median of series values within the time interval [t-w, t+w] is calculated. The corresponding value is named (2*w+1)-pointwise moving median. The major advantage of median smoothing is its insensitivity to outliers.

If the time moment t is less than w points from the beginning or the end of the series, the calculation becomes impossible. To eliminate these edge effects (except for end points), the moving median of the minor highest possible order is calculated. This enables the user not to narrow the domain of the smoothed series compared to the source series. The end values are processed using the Tukey procedure. According to this procedure the median of three points X0, X1 and (3X1-2X2) must be taken as a smoothed value for X0 (0 - start moment); the formula is similar for the end moment. Using this procedure, any set of moving medians (from 3-point median to 23-point median) can be applied to the source series. Procedures are applied in order of decreasing window width.