The Onset Trend Detector study is a trend analyzing technical indicator developed by John F. Ehlers, based on a non-linear quotient transform. Two of Mr. Ehlers' previous studies, the Super Smoother Filter and the Roofing Filter, were used and expanded to create this new complex technical indicator. Being a trend-following analysis technique, its main purpose is to address the problem of lag that is common among moving average type indicators.

The Onset Trend Detector first applies the EhlersRoofingFilter to the input data in order to eliminate cyclic components with periods longer than, for example, 100 bars (default value, customizable via input parameters) as those are considered spectral dilation. Filtered data is then subjected to re-filtering by the Super Smoother Filter so that the noise (cyclic components with low length) is reduced to minimum. The period of 10 bars is a default maximum value for a wave cycle to be considered noise; it can be customized via input parameters as well. Once the data is cleared of both noise and spectral dilation, the filter processes it with the automatic gain control algorithm which is widely used in digital signal processing. This algorithm registers the most recent peak value and normalizes it; the normalized value slowly decays until the next peak swing. The ratio of previously filtered value to the corresponding peak value is then quotiently transformed to provide the resulting oscillator. The quotient transform is controlled by the K coefficient: its allowed values are in the range from -1 to +1. K values close to 1 leave the ratio almost untouched, those close to -1 will translate it to around the additive inverse, and those close to zero will collapse small values of the ratio while keeping the higher values high.

Indicator values around 1 signify uptrend and those around -1, downtrend.

Input Parameters

price Defines the price to which the oscillator is applied.
cutoff length Defines the minimum cycle length in bars. Cycles with lesser lengths will be considered noise and eliminated.

roof cutoff length

Defines the maximum cycle length in bars. Cycles with greater lengths will be considered spectral dilation and eliminated.


The K coefficient used in quotient transform.


NormRoofingFilter The normalized Roofing Filter plot.
Quotient The quotient transform plot.


The zero level.

Further Reading

1. "The Quotient Transform" by John F. Ehlers. Technical Analysis of Stocks & Commodities, August 2014.


*For illustrative purposes only. Not a recommendation of a specific security or investment strategy.

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