Laguerre Filter Pass Node

4-Pole Laguerre Filter — Series Input

MomentumSmoothingPass

Overview

The Laguerre Filter Pass Node applies a 4-pole Laguerre recursive filter to a series input. This filter achieves significant smoothing with minimal lag by using a single gamma coefficient to control the frequency response across all four poles.

Developed by John Ehlers, the Laguerre Filter uses an orthogonal basis to construct a causal low-pass filter that outperforms simple moving averages. A higher gamma value increases smoothing but adds more lag; lower gamma tracks price more closely. Because it is fully recursive, output begins from bar 0 with no fixed warm-up period.

Formula

L0[i] = (1 − gamma) × price[i] + gamma × L0[i−1]
L1[i] = −gamma × L0[i] + L0[i−1] + gamma × L1[i−1]
L2[i] = −gamma × L1[i] + L1[i−1] + gamma × L2[i−1]
L3[i] = −gamma × L2[i] + L2[i−1] + gamma × L3[i−1]
Filter[i] = (L0 + 2×L1 + 2×L2 + L3) / 6
No fixed warm-up — recursive from bar 0. Output range: unbounded (tracks price).

Parameters

ParameterDefaultDescription
gamma0.8Damping coefficient (0–1). Higher = more smoothing, more lag

Inputs & Outputs

SlotDirectionTypeDescription
inputInput{ values, timestamps }Price or any numeric series
valuesOutputnumber[]Smoothed Laguerre filter values; valid from bar 0
timestampsOutputnumber[]Unix timestamps aligned to input

Use Cases

Low-Lag Trend Following

Use the Laguerre Filter as a trailing trend line that reacts faster than an equivalent-smoothness EMA — crossovers of price above/below the filter generate trend signals with less noise.

Noise Reduction Preprocessing

Pipe the Laguerre Filter output into other indicators instead of raw price — reduces noise in RSI, ROC, or divergence calculations without the lag penalty of a standard SMA or EMA.

Dynamic Support / Resistance

The Laguerre Filter output at any gamma > 0.7 acts as a smooth dynamic support/resistance level — bounces off the filter in trending markets can confirm continuation entries.

Tips & Best Practices

Gamma Tuning

gamma=0.5 provides moderate smoothing; gamma=0.8 is heavy smoothing for long-term trends; gamma=0.2 is nearly as reactive as price. Tune by visually matching the filter to the desired cycle.

No Warm-Up Advantage

Unlike period-based indicators, the Laguerre Filter produces valid output from bar 0. This is a significant advantage for short data series or the beginning of a new symbol's history.

Use with Laguerre RSI

The Laguerre Filter is the foundation of the Laguerre RSI. Use both at the same gamma for a consistent Ehlers-based system — the filter as trend line and Laguerre RSI as oscillator.

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