FourierDominantCycle
Dominant cycle period estimation using resolution-enhanced DFT and center of gravity.
Usage
Use to compute the dominant market cycle period via DFT. Feed the output period into adaptive indicators like DSMA or Ehlers Stochastic to make them cycle-synchronized.
Background
Ehlers implements a Discrete Fourier Transform cycle measurement in Cybernetic Analysis using a Hann-windowed data segment. The DFT computes power across periods from 6 to 50 bars, and the peak power identifies the dominant cycle period driving price movement.
Parameters
window_len(default: 50): DFT window length
Formula
[ HP = \text{HighPass}(Price, 40) ] [ Cleaned = \frac{HP + 2HP_{t-1} + 3HP_{t-2} + 3HP_{t-3} + 2HP_{t-4} + HP_{t-5}}{12} ] [ Pwr(P) = \left(\sum_{n=0}^{W-1} Cleaned_{t-n} \cos\left(\frac{2\pi n}{P}\right)\right)^2 + \left(\sum_{n=0}^{W-1} Cleaned_{t-n} \sin\left(\frac{2\pi n}{P}\right)\right)^2 ] [ DB(P) = \min\left(20, -10 \log_{10}\left(\frac{0.01}{1 - 0.99 \frac{Pwr(P)}{\max(Pwr)}}\right)\right) ] [ DC = \frac{\sum_{P=8}^{50} P \cdot (3 - DB(P)) \text{ where } DB(P) < 3}{\sum (3 - DB(P))} ]