Hilbert Transform - Dominant Cycle Phase (HT_DCPHASE)

Ehlers DSP cycle hilbert phase dsp

Calculates the phase angle (0 to 360 degrees) of the dominant cycle identified by the Hilbert Transform.

Visual Example

Hilbert Transform - Dominant Cycle Phase (HT_DCPHASE) — 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

Calculates the phase angle (0 to 360 degrees) of the dominant cycle identified by the Hilbert Transform.

Use to identify the current position within a market cycle. It is the core component for generating the Hilbert Sine Wave indicator, which signals trend vs. cycle regimes.

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.

The Dominant Cycle Phase represents the instantaneous position within a detected cycle. By measuring the phase angle, traders can determine if the market is at a peak, trough, or mid-cycle, enabling more precise timing for entry and exit signals. — Rocket Science for Traders

Typical applications:

Use for cycle timing in mean-reverting regimes
Gate with Hurst exponent or ADX before taking cycle signals
Allow N+ 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/cycle.rs):

\[ Phase = \arctan\left(\frac{\text{Quadrature}}{\text{InPhase}}\right) \]

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

Parameters

Parameter	Default	Description
(none)	—	No tunable parameters for this detector.

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::HT_DCPHASE;
use quantwave_core::traits::Next;

let mut ind = HT_DCPHASE::new(14);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import HT_DCPHASE

ind = HT_DCPHASE(14)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave  # registers pl.col().ta

df = (
    pl.read_csv('ohlcv.csv')
    .lazy()
    .with_columns(
        pl.col("close").ta.ht_dcphase(14).alias("hilbert_transform_dominant_cycle_phase_ht_dcphase")
    )
    .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://www.tradingview.com/support/solutions/43000502010-hilbert-transform-dominant-cycle-phase-ht-dcphase/

Implementation: quantwave-core/src/indicators/cycle.rs (HT_DCPHASE / HT_DCPHASE_METADATA). Parity: quantwave-core/tests/gold_standard/ht_dcphase.json

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