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FourierDominantCycle

Ehlers DSP cycle spectral ehlers dsp dominant-cycle fourier

Dominant cycle period estimation using resolution-enhanced DFT and center of gravity.

Visual Example

FourierDominantCycle — annotated preview mapping to core implementation

Synthetic ideal per library logic. Generated 2026-07-01 IST via docs/generate_all_previews.py (reproducible; maps to core Next<T> implementation).

Description

Dominant cycle period estimation using resolution-enhanced DFT and center of gravity.

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.

Part of QuantWave's Ehlers digital signal processing suite. Designed for low-lag cycle and trend work — pair with Roofing Filter or SuperSmoother on noisy inputs.

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.

Typical applications:

  • Use for cycle timing in mean-reverting regimes
  • Gate with Hurst exponent or ADX before taking cycle signals
  • Allow 50+ bars warm-up for filter state to stabilise
  • Chain with Roofing Filter when input is noisy

QuantWave implements this via the universal Next<T> trait — bit-identical across Rust streaming, Python streaming, and Polars .ta() batch plugins.

Formula / Specification

Implementation (quantwave-core/src/indicators/fourier_transform.rs):

[ 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))} ]

Gold-standard parity vectors: quantwave-core/tests/gold_standard/fourier_dominant_cycle.json.

Parameters

Parameter Default Description
window_len 50 DFT window length

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::FOURIER_DOMINANT_CYCLE;
use quantwave_core::traits::Next;

let mut ind = FOURIER_DOMINANT_CYCLE::new(50);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import FOURIER_DOMINANT_CYCLE

ind = FOURIER_DOMINANT_CYCLE(50)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_fourierdominantcycle(series: pl.Series) -> pl.Series:
    ind = qw.FOURIER_DOMINANT_CYCLE(50)
    return pl.Series([ind.next(float(v)) for v in series.to_list()])

df = (
    pl.read_csv('ohlcv.csv')
    .lazy()
    .with_columns(
        pl.col("close").map_batches(apply_fourierdominantcycle, return_dtype=pl.Float64).alias("fourierdominantcycle")
    )
    .collect()
)

All surfaces are bit-identical via the single Next<T> implementation and proptests.

Edge Cases & Limitations

  • Recursive DSP filters require a warm-up period; first N bars may be unstable or raw-pass-through.
  • Designed for cyclic/mean-reverting regimes; trending markets can produce lag or drift.
  • Parameter period (or equivalent) controls cutoff — too small adds noise, too large adds lag.
  • Prefer chaining with other Ehlers tools (Roofing Filter, SuperSmoother) on noisy inputs.
  • Validated via proptests against gold-standard vectors where available.
  • No look-ahead bias; suitable for live streaming and batch feature pipelines.

Boundary Behavior

Condition Behavior
Warm-up Leading bars return NaN until warmup_bars is satisfied.
period > len When period exceeds series length, output is all NaN.
NaN inputs NaN in input propagates to output (NaN out).
Invalid params Non-positive period or missing required params raise ValueError.
Empty data Empty input returns an empty result series.

Sources & References

Primary Source: https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/FourierTransformForTraders.pdf

Implementation: quantwave-core/src/indicators/fourier_transform.rs (FOURIER_DOMINANT_CYCLE / FOURIER_DOMINANT_CYCLE_METADATA). Parity: quantwave-core/tests/gold_standard/fourier_dominant_cycle.json

Provenance: Standards bulk upgrade 2026-07-01 IST — see docs/DOCUMENTATION_STANDARDS.md.