BandPass
A bandpass filter that isolates cycle components around a center period.
Usage
Apply to isolate a specific cycle period in price, filtering out both trend and noise. Use zero crossings of the filtered output as entry and exit signals.
Background
Ehlers presents the BandPass filter in Cybernetic Analysis as a second-order IIR filter centred on a target cycle period with tunable bandwidth. It simultaneously attenuates lower and higher frequencies, leaving only the desired cycle band in the output.
Parameters
period(default: 20): Center period of the passbandbandwidth(default: 0.1): Relative bandwidth (delta)
Formula
[ \beta = \cos(360/P), \gamma = 1/\cos(720\delta/P), \alpha = \gamma - \sqrt{\gamma^2 - 1} ] [ BP = 0.5(1 - \alpha)(Price - Price_{t-2}) + \beta(1 + \alpha)BP_{t-1} - \alpha BP_{t-2} ]