Laguerre Filter Pass Node
4-Pole Laguerre Filter — Series Input
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
Parameters
| Parameter | Default | Description |
|---|---|---|
| gamma | 0.8 | Damping coefficient (0–1). Higher = more smoothing, more lag |
Inputs & Outputs
| Slot | Direction | Type | Description |
|---|---|---|---|
| input | Input | { values, timestamps } | Price or any numeric series |
| values | Output | number[] | Smoothed Laguerre filter values; valid from bar 0 |
| timestamps | Output | number[] | 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.