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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 2026-07-01 IST via docs/generate_all_previews.py (reproducible; maps to core Next<T> implementation).

Description

2-pole Butterworth low-pass filter.

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.

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.

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.

Typical applications:

  • Use for cycle timing in mean-reverting regimes
  • Gate with Hurst exponent or ADX before taking cycle signals
  • Allow 14+ 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/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 2026-07-01 IST — see docs/DOCUMENTATION_STANDARDS.md.