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Classic Laguerre Filter

Ehlers DSP filter ehlers dsp smoothing laguerre

The original Laguerre filter from John Ehlers' 2002 'Time Warp' paper.

Visual Example

Classic Laguerre 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

The original Laguerre filter from John Ehlers' 2002 'Time Warp' paper.

Use when a smooth trend estimate with controllable lag using only 4 state variables is needed. Preferred over long EMAs when computational memory is constrained.

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 Classic Laguerre Filter uses four first-order IIR sections sharing the same gamma coefficient. In Cybernetic Analysis (2004) Ehlers shows gamma maps directly to an effective period, making it highly tunable with minimal computation.

Typical applications:

  • Use for cycle timing in mean-reverting regimes
  • Gate with Hurst exponent or ADX before taking cycle signals
  • Allow 0.8+ 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/classic_laguerre.rs):

[ L_0 = (1 - \gamma) \cdot Price + \gamma \cdot L_{0,t-1} ] [ L_1 = -\gamma L_0 + L_{0,t-1} + \gamma L_{1,t-1} ] [ L_2 = -\gamma L_1 + L_{1,t-1} + \gamma L_{2,t-1} ] [ L_3 = -\gamma L_2 + L_{2,t-1} + \gamma L_{3,t-1} ] [ Filt = \frac{L_0 + 2L_1 + 2L_2 + L_3}{6} ]

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

Parameters

Parameter Default Description
gamma 0.8 Smoothing factor (0.0 to 1.0)

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::CLASSIC_LAGUERRE;
use quantwave_core::traits::Next;

let mut ind = CLASSIC_LAGUERRE::new(0.8);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import CLASSIC_LAGUERRE

ind = CLASSIC_LAGUERRE(0.8)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_classic_laguerre_filter(series: pl.Series) -> pl.Series:
    ind = qw.CLASSIC_LAGUERRE(0.8)
    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_classic_laguerre_filter, return_dtype=pl.Float64).alias("classic_laguerre_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/Ehlers%20Papers/TimeWarp.pdf

Implementation: quantwave-core/src/indicators/classic_laguerre.rs (CLASSIC_LAGUERRE / CLASSIC_LAGUERRE_METADATA). Parity: quantwave-core/tests/gold_standard/classic_laguerre.json

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