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Synthetic Oscillator

Ehlers DSP oscillator ehlers dsp cycle synthetic

A nonlinear oscillator designed to reduce lag while maintaining smoothness by adapting to the dominant cycle.

Visual Example

Synthetic Oscillator — 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

A nonlinear oscillator designed to reduce lag while maintaining smoothness by adapting to the dominant cycle.

Use to construct a synthetic oscillator from dominant cycle sine components when direct price oscillators are too noisy. Most effective in clearly cyclical markets.

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 constructs a Synthetic Oscillator by generating a synthetic sine wave at the measured dominant cycle period and comparing it to price. The phase difference between the synthetic sine and actual price reveals whether the market is ahead of or behind its expected cycle position.

Typical applications:

  • Use for cycle timing in mean-reverting regimes
  • Gate with Hurst exponent or ADX before taking cycle signals
  • Allow 15+ 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/synthetic_oscillator.rs):

[ Price = \text{Hann}(Close, 12) ] [ LP = \text{SuperSmoother}(\text{HighPass}(Price, UB), LB) ] [ Re = \frac{LP}{RMS(LP, 100)}, \quad Im = \frac{Re - Re_{t-1}}{RMS(Re - Re_{t-1}, 100)} ] [ DC = \frac{2\pi(Re^2 + Im^2)}{(Re - Re_{t-1})Im - (Im - Im_{t-1})Re} ] [ BP = \text{UltimateSmoother}(\text{HighPass}(Close, Mid), Mid) ] [ Phase = Phase_{t-1} + \frac{2\pi}{DC} ] [ Synth = \sin(Phase) ]

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

Parameters

Parameter Default Description
lower_bound 15 Lower bound of cycle period
upper_bound 25 Upper bound of cycle period

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::SYNTHETIC_OSCILLATOR;
use quantwave_core::traits::Next;

let mut ind = SYNTHETIC_OSCILLATOR::new(15);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import SYNTHETIC_OSCILLATOR

ind = SYNTHETIC_OSCILLATOR(15)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_synthetic_oscillator(series: pl.Series) -> pl.Series:
    ind = qw.SYNTHETIC_OSCILLATOR(15)
    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_synthetic_oscillator, return_dtype=pl.Float64).alias("synthetic_oscillator")
    )
    .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/traderstipsreference/TRADERS’%20TIPS%20-%20APRIL%202026.html

Implementation: quantwave-core/src/indicators/synthetic_oscillator.rs (SYNTHETIC_OSCILLATOR / SYNTHETIC_OSCILLATOR_METADATA). Parity: quantwave-core/tests/gold_standard/synthetic_oscillator.json

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