Skip to content

GaussianFilter

Ehlers DSP filter smoothing ehlers dsp low-pass

Multi-pole Gaussian low-pass filter for reduced lag.

Visual Example

GaussianFilter — 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 GaussianFilter indicator is a technical analysis tool that multi-pole gaussian low-pass filter for reduced lag.

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 when smooth symmetric price averaging with near-zero phase shift is needed. Works well as a preprocessing step for spectral analysis indicators.

Gaussian filters are the theoretically optimal lowpass filter for minimizing the product of time-domain duration and frequency-domain bandwidth. Ehlers implements them as cascaded pole filters with Gaussian-function-derived coefficients, achieving very smooth output with excellent stopband attenuation.

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/gaussian.rs):

[ \alpha = -\beta + \sqrt{\beta^2 + 2\beta} ] [ \beta = \frac{1 - \cos(2\pi/P)}{2^{1/(2N)} - 1} ]

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

Parameters

Parameter Default Description
period 14 Critical period
poles 4 Number of poles (1-4)

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::GAUSSIAN_FILTER;
use quantwave_core::traits::Next;

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

Streaming (Python)

from quantwave import GAUSSIAN_FILTER

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

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_gaussianfilter(series: pl.Series) -> pl.Series:
    ind = qw.GAUSSIAN_FILTER(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_gaussianfilter, return_dtype=pl.Float64).alias("gaussianfilter")
    )
    .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/GaussianFilters.pdf

Implementation: quantwave-core/src/indicators/gaussian.rs (GAUSSIAN_FILTER / GAUSSIAN_FILTER_METADATA). Parity: quantwave-core/tests/gold_standard/gaussian_filter.json

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