# Gaussian Filter MACD [Loxx]

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Gaussian Filter MACD is a MACD that uses an 1-4 Pole Ehlers Gaussian Filter for its calculations. Compare this with Ehlers Fisher Transform.

What is Ehlers Gaussian filter?
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 Wealth-Lab by Dr René Koch.

A Gaussian filter is one whose transfer response is described by the familiar Gaussian bell-shaped curve. In the case of low-pass 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 high-frequency components relative to the lag of lower-frequency 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 high-frequency components in the eprice data. Therefore these smoothers are called low-pass filters, and they all work by some form of averaging. Butterworth low-pass 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"

Included
• Loxx's Expanded Source Types
• Signals, zero or signal crossing, signal crossing is very noisy
• Bar coloring
Notes de version:
Updated formulas.