Although not part of the original question, the posted diagram appears to be smoothing the Bollinger (StdDev.Series) Bands with a Gaussian filter as well.  The link 
http://www.indicatorsmt4.com/indicators/gaussian-bands/ confirms this.  Simply take the posted solution and add a line to 
optionally run the resulting StdDev DataSeries through the Gaussian filter (indicator) as well.
The transfer function for any digital filter comes in two parts: A numerator characteristic equation and a denominator characteristic equation.  The roots to the numerator equation are calls "zeros" and the roots to the denominator equation are called "poles".  These roots define the smoothing points of the filter in the "frequency" (
not the "time") domain.
For the low-pass Gaussian filter mentioned (which only has a denominator equation), adding more poles to the filter will 
both increase the smoothing and the sharpness of its high-frequency cutoff.