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One Euro Filter

Ehlers DSP filter smoothing adaptive real-time low-pass

A speed-based adaptive low-pass filter that dynamically adjusts its smoothing coefficient.

Visual Example

One Euro Filter — 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 speed-based adaptive low-pass filter that dynamically adjusts its smoothing coefficient.

Use in real-time systems where you need low lag at high speeds and low noise at low speeds. The adaptive cutoff frequency makes it self-tuning for different signal velocities.

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 One Euro Filter, developed by Casiez et al. (2012), is an adaptive lowpass filter that adjusts its cutoff frequency based on the signal derivative. When the signal changes quickly (high speed) the cutoff is raised to reduce lag; when it changes slowly the cutoff is lowered to reduce noise — automatically balancing the speed-accuracy trade-off.

Typical applications:

  • Use for cycle timing in mean-reverting regimes
  • Gate with Hurst exponent or ADX before taking cycle signals
  • Allow 10+ 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/one_euro_filter.rs):

[ \alpha_{dx} = \frac{2\pi}{4\pi + 10} ] [ SmoothedDX = \alpha_{dx}(Price - Price_{t-1}) + (1 - \alpha_{dx})SmoothedDX_{t-1} ] [ Cutoff = PeriodMin + \beta |SmoothedDX| ] [ \alpha_3 = \frac{2\pi}{4\pi + Cutoff} ] [ Smoothed = \alpha_3 Price + (1 - \alpha_3)Smoothed_{t-1} ]

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

Parameters

Parameter Default Description
period_min 10 Minimum cutoff period
beta 0.2 Responsiveness factor

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::ONE_EURO_FILTER;
use quantwave_core::traits::Next;

let mut ind = ONE_EURO_FILTER::new(10);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import ONE_EURO_FILTER

ind = ONE_EURO_FILTER(10)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_one_euro_filter(series: pl.Series) -> pl.Series:
    ind = qw.ONE_EURO_FILTER(10)
    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_one_euro_filter, return_dtype=pl.Float64).alias("one_euro_filter")
    )
    .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-%20DECEMBER%202025.html

Implementation: quantwave-core/src/indicators/one_euro_filter.rs (ONE_EURO_FILTER / ONE_EURO_FILTER_METADATA). Parity: quantwave-core/tests/gold_standard/one_euro_filter.json

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