HighPass
A second-order High Pass filter that rejects low-frequency components.
Usage
Apply to price to isolate the cyclical component by attenuating the low-frequency trend. Use as the first stage before an oscillator or spectrum analyser.
Background
Ehlers derives the one-pole high-pass filter in Cycle Analytics for Traders analogously to EMA derivation, but applied to price differences rather than levels. It removes the DC component and low-frequency trend, leaving the cyclical content for downstream analysis.
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) / 4 ] [ HP = c_1 (Price - 2 Price_{t-1} + Price_{t-2}) + c_2 HP_{t-1} + c_3 HP_{t-2} ]