Butterworth3
3-pole Butterworth low-pass filter.
Usage
Use to smooth price or intermediate indicator values with a flat passband and sharp rolloff. The 3-pole version provides steeper attenuation at the cost of marginally more lag.
Background
Butterworth filters are maximally flat in the passband, introducing no ripple. Ehlers implements 2-pole and 3-pole Butterworth IIR designs in Cycle Analytics for Traders, noting that the SuperSmoother is actually a critically-damped 2-pole Butterworth variant.
Parameters
period(default: 14): Critical period
Formula
[ a = \exp(-\pi/P) ] [ b = 2a \cos(1.738\pi/P) ] [ c = a^2 ] [ f = (b+c)f_{t-1} - (c+bc)f_{t-2} + c^2f_{t-3} + \frac{(1-b+c)(1-c)}{8}(g + 3g_{t-1} + 3g_{t-2} + g_{t-3}) ]