[blackcat] L2 Ehlers Zero Crossings Period Measurer

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Level: 2


John F. Ehlers introuced Zero Crossings Period Measurer in his "Cycle Analytics for Traders" chapter 5 on 2004.


The band-pass filter can be used as a relatively simple measurement of the dominant cycle. A cycle is complete when the waveform crosses zero two times from the last zero crossing. Therefore, each successive zero crossing of the indicator marks a half cycle period. We can establish the dominant cycle period as twice the spacing between successive zero crossings. When we measure the dominant cycle period this way, it is best to widen the pass band of the band-pass filter to avoid distorting the measurement simply due to the selectivity of the filter. Using an input bandwidth of 0.7 produces an octave-wide pass band. For example, if the center period of the filter is 20 and the relative bandwidth is 0.7, the bandwidth is 14. That means the pass band of the filter extends from 13-bar periods to 27-bar periods. That is, roughly an octave exists because the longest period is twice the shortest period of the pass band. It is imperative that a high-pass filter is tuned one octave below the halfbandwidth edge of the band-pass filter to ensure a nominal zero mean of the filtered output. Without a zero mean, the zero crossings can have a substantial error.

Key Signal

DC ---> dominant cycle

Pros and Cons

100% John F. Ehlers definition translation of original work, even variable names are the same. This help readers who would like to use pine to read his book. If you had read his works, then you will be quite familiar with my code style.


The 39th script for Blackcat1402 John F. Ehlers Week publication.


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Nota Keluaran:
I noticed there are some errors in Ehlers books' description on counter part. It was correctly and the function is now the same as the figure in Ehlers book now.

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