Syntax
public Gaussian(DataSeries ds, double period, int poles, string description)
public static Gaussian Series(DataSeries ds, double period, int poles)
Parameter Description
ds 
Source Series 
period 
The critical period of the filter. Price movements (cycles) with this period are attenuated by 50% (3 dB). Note that in this case, period can be a floating point number.

poles 
The number of poles of the filter. Must be 1, 2, 3 or 4.

Description
This filter can be used for smoothing. It rejects high frequencies (fast movements) better than an EMA and has lower lag.
published by John F. Ehlers in "Rocket Science For Traders". First implemented in WealthLab by Dr RenĂ© Koch.
A Gaussian filter is one whose transfer response is described by the familiar Gaussian bellshaped curve. In the case of lowpass filters, only the upper half of the curve describes the filter. The use of gaussian filters is a move toward achieving the dual goal of reducing lag and reducing the lag of highfrequency components relative to the lag of lowerfrequency components.
A gaussian filter with...
 one pole is equivalent to an EMA filter.
 two poles is equivalent to EMA(EMA())
 three poles is equivalent to EMA(EMA(EMA()))
 and so on...
For an equivalent number of poles the lag of a Gaussian is about half the lag of a Butterworth filters:
Lag = N * P / (2 * ¶
^{2}), where,
N is the number of poles, and
P is the critical period
Special initialization of filter stages ensures proper working in scans with as few bars as possible.
From Ehlers Book: "The first objective of using smoothers is to eliminate or reduce the undesired highfrequency components in the eprice data. Therefore these smoothers are called lowpass filters, and they all work by some form of averaging. Butterworth lowpass filtters can do this job, but nothing comes for free. A higher degree of filtering is necessarily accompanied by a larger amount of lag. We have come to see that is a fact of life."
References
John F. Ehlers: "Rocket Science For Traders, Digital Signal Processing Applications", Chapter 15: "Infinite Impulse Response Filters"
Example