Two Pole Butterworth Filter

The Two Pole Butterworth Filter (TPBF) was authored by John Ehlers. The TPBF uses current price, previous prices and feedback in its calculation. The user may change the input (close) and period length. This indicator’s definition is further expressed in the condensed code given in the calculation below.

How To Trade Using Two Pole Butterworth Filter

The Two Pole Butterworth Filter is a trend indicator and may be used in conjunction with other studies. No trading signals are calculated.

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Go to the top menu, choose Study>John Ehlers>Two Pole Butterworth Filter

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Calculation

//input = price, user defined, default is closing price
//period = user defined, default is 20
//prev = previous, index = current bar number

prevP1 = price[index-1];
prevP2 = price[index-2];
prevB1 = ifNull(price, butter[index-1]);  //feedback ingredent
prevB2 = ifNull(price, butter[index-2]);  //feedback ingredent
piPrd = Math.PI/period;
a1 = Math.exp(-1.414 * piPrd);
b1 = 2 * a1 * Math.cos(1.414 * piPrd);
coef2 = b1;
coef3 = -a1 * a1;
coef1 = (1 - b1 + a1 * a1) / 4;
plot: butter = coef1 * (price + (2*prevP1) + prevP2) + (coef2*prevB1) + (coef3*prevB2);