[blackcat] L2 Ehlers Three Pole Butterworth Filter

Level: 2

Background

John F. Ehlers introuced Three-Pole Butterworth Filter in his "Cybernetic Analysis for Stocks and Futures" chapter 13 on 2004.


Function

The transfer responses of Butterworth filters have polynomials in both the numerator and denominator. There is a polynomial in the numerator as well as the denominator. The significance of the polynomial in the numerator is that it represents the finite impulse response (FIR) part of the filter. This part is like a simple moving average. The denominator forms the iterative part of the filter calculation and is the infinite impulse response (IIR) part of the filter. The FIR part of the filter sharpens the filter rejection response, but it also contributes to lag in the response. Recognizing that the parts of a Butterworth filter are separable, Dr. Ehlers formed the multipole super smoothing filters by simply deleting the polynomial in the numerator. Butterworth filters can have an arbitrarily large number of poles. The passband of Butterworth filters is prescribed by a single parameter. That parameter is the Cutoff Period, where the attenuation of the filter is 3 dB.


Key Signal

Butter ---> Two Pole Butterworth Filter fast line
Trigger ---> Two Pole Butterworth Filter slow line


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.

Remarks

The 30th script for Blackcat1402 John F. Ehlers Week publication.

Readme

In real life, I am a prolific inventor. I have successfully applied for more than 60 international and regional patents in the past 12 years. But in the past two years or so, I have tried to transfer my creativity to the development of trading strategies. Tradingview is the ideal platform for me. I am selecting and contributing some of the hundreds of scripts to publish in Tradingview community. Welcome everyone to interact with me to discuss these interesting pine scripts.

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Level 4 : script snippets or functions that do not disclose source code. Interesting element that can reveal market laws and work as raw material for indicators and strategies. If you find Level 1~2 scripts are helpful, Level 4 is a private version that took me far more efforts to develop.

Level 5 : indicator/strategy that do not disclose source code. private version of Level 3 script with my accumulated script processing skills or a large number of custom functions. I had a private function library built in past two years. Level 5 scripts use many of them to achieve private trading strategy.

Nota Keluaran:

thanks to @sal157011 reminding, i corrected line #37 into Butter := coef1*(Price + 3*nz(Price(1)) + 3*nz(Price(2)) + nz(Price(3))) + coef2*nz(Butter(1)) + coef3*nz(Butter(2)) + coef4*nz(Butter(3))