SuperSmoother
A second-order IIR filter with a maximally flat Butterworth response for superior smoothing with minimal lag.
Usage
Use as a drop-in replacement for any moving average when maximum smoothing with minimal lag is needed. Ideal as a pre-filter before oscillators to eliminate high-frequency noise.
Background
Ehlers describes the SuperSmoother as a two-pole Butterworth filter achieving the same smoothing as a longer SMA with far less lag. It uses a critically-damped design to eliminate Gibbs phenomenon overshoot while retaining cycle information. — Cybernetic Analysis for Stocks and Futures, 2004
Parameters
period(default: 20): Critical period (wavelength)
Formula
[ a_1 = \exp\left(-\frac{1.414\pi}{Period}\right) ] [ c_2 = 2a_1 \cos\left(\frac{1.414\pi}{Period}\right) ] [ c_3 = -a_1^2 ] [ c_1 = 1 - c_2 - c_3 ] [ SS = c_1 \frac{Price + Price_{t-1}}{2} + c_2 SS_{t-1} + c_3 SS_{t-2} ]