Butterworth2

Ehlers DSP filter ehlers dsp smoothing low-pass

2-pole Butterworth low-pass filter.

Visual Example

Butterworth2 — annotated preview mapping to core implementation

Synthetic ideal per library logic. Generated 2026-06-25 IST via docs/generate_all_previews.py (reproducible; maps to core Next<T> implementation).

Description

The Butterworth2 indicator is a technical analysis tool that 2-pole butterworth low-pass filter.

This indicator is primarily used for identifying key market conditions. It provides a robust signal that can be easily integrated into both simple strategies and more complex machine learning feature pipelines. Compared to its alternatives, it offers a distinct balance of responsiveness and stability.

Traders often combine this with other metrics to confirm signals and avoid false positives during sideways market regimes. It remains a standard tool for systematic trading models.

Use to smooth price or intermediate indicator values with a flat passband and sharp rolloff. The 3-pole version provides steeper attenuation at the cost of marginally more lag.

Butterworth filters are maximally flat in the passband, introducing no ripple. Ehlers implements 2-pole and 3-pole Butterworth IIR designs in Cycle Analytics for Traders, noting that the SuperSmoother is actually a critically-damped 2-pole Butterworth variant.

QuantWave implements this indicator via the universal Next<T> trait, guaranteeing bit-identical results between Rust streaming, Python streaming, and Polars batch (.ta() / map_batches) surfaces.

Formula / Specification

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

[ a = \exp(-1.414\pi/P) ] [ b = 2a \cos(1.414\pi/P) ] [ f = bf_{t-1} - a^2f_{t-2} + \frac{1-b+a^2}{4}(g + 2g_{t-1} + g_{t-2}) ]

Gold-standard parity vectors: quantwave-core/tests/gold_standard/butterworth2.json.

Parameters

Parameter	Default	Description
`period`	14	Critical period

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::BUTTERWORTH2;
use quantwave_core::traits::Next;

let mut ind = BUTTERWORTH2::new(14);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import BUTTERWORTH2

ind = BUTTERWORTH2(14)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_butterworth2(series: pl.Series) -> pl.Series:
    ind = qw.BUTTERWORTH2(14)
    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_butterworth2, return_dtype=pl.Float64).alias("butterworth2")
    )
    .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/Poles.pdf

Implementation: quantwave-core/src/indicators/butterworth.rs (BUTTERWORTH2 / BUTTERWORTH2_METADATA). Parity: quantwave-core/tests/gold_standard/butterworth2.json

Provenance: Standards bulk upgrade 2026-06-25 IST — see docs/DOCUMENTATION_STANDARDS.md.