SuperSmoother

John Ehlers' 2-pole Butterworth-style lowpass filter. Critically damped, so it removes high-frequency noise without ringing, overshoot, or the boxy step response of a simple SMA. The standard Ehlers pre-filter to put in front of any cycle-aware oscillator.

Quick reference

Item	Value
Family	Ehlers / Cycle (DSP)
Input type	f64
Output type	f64
Output range	unbounded; tracks input scale
Default parameters	period is required (typical 10)
Warmup period	2 (uses the input directly for the first two bars)
Interpretation	Lowpass-filtered price; passes periods longer than period

Formula

For a given critical period period, the filter coefficients are:

a1 = exp(-sqrt(2) · π / period)
b1 = 2 · a1 · cos(sqrt(2) · π / period)
c2 = b1
c3 = -a1²
c1 = 1 - c2 - c3

y_t = c1 · (x_t + x_{t-1}) / 2 + c2 · y_{t-1} + c3 · y_{t-2}

The implementation needs two prior inputs and two prior outputs to begin running; until then it returns the input itself (the Ehlers- standard initial condition), which lets downstream filters warm up without long delays. See crates/wickra-core/src/indicators/super_smoother.rs.

Parameters

Name	Type	Default	Constraint	Description
period	usize	none	> 1	Critical period — the boundary above which signal is passed.

SuperSmoother::new returns Error::PeriodZero for period == 0 and Error::InvalidPeriod for period == 1 (no smoothing possible).

Inputs / Outputs

Indicator<Input = f64, Output = f64>. Python: SuperSmoother(period).batch(prices) returns a 1-D np.ndarray without warmup NaNs (Ehlers' "pass through input" initial condition). Node: same shape; update(value) returns number.

Warmup

warmup_period() == 2. The first two inputs return the input itself; from input 3 onwards the proper 2-pole recursion runs. By input ~2 · period the initial transient has decayed.

Edge cases

• Constant input. Output converges to the constant.
• Step input. Critically damped — no overshoot, no ringing. Roughly 0.7 · period bars to reach 99% of the new level.
• Sinusoid at the critical period. Output is attenuated by ~3 dB (≈ 70%) — the canonical cutoff.
• High-frequency noise. Suppressed at >20 dB for periods shorter than period / 4.
• Reset. reset() clears all prior inputs and outputs to None and resets the bar counter.

Examples

Rust

use wickra::{BatchExt, Indicator, SuperSmoother};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let prices: Vec<f64> = (0..80)
        .map(|i| 100.0 + (f64::from(i) * 1.5).sin() * 5.0)
        .collect();
    let mut ss = SuperSmoother::new(10)?;
    println!("row 20 = {:?}", ss.batch(&prices)[20]);
    Ok(())
}

Python

import numpy as np
import wickra as ta

# Noisy price with both a slow trend and high-frequency noise
t = np.arange(200)
prices = 100 + np.sin(t * 0.1) * 5 + np.random.normal(0, 0.5, 200)
ss = ta.SuperSmoother(10)
out = ss.batch(prices)
print('row 50:', out[50])

Node

const wickra = require('wickra');

const ss = new wickra.SuperSmoother(10);
const prices = Array.from({ length: 200 },
  (_, i) => 100 + Math.sin(i * 0.1) * 5);
console.log('row 50:', ss.batch(prices)[50]);

Streaming

use wickra::{Indicator, SuperSmoother};

let mut ss = SuperSmoother::new(10).unwrap();
let price_stream: Vec<f64> = Vec::new(); // your live price feed
for px in price_stream {
    let smoothed = ss.update(px).unwrap();
    // Use as a noise-suppressed price signal for downstream logic
}

Interpretation

• Lowpass building block. Use SuperSmoother as a noise filter in front of oscillators that are sensitive to bar-to-bar noise (RSI, Stochastic, CCI). The cleaner input often eliminates the need for the oscillator's own smoothing pass.
• Vs SMA / EMA. SuperSmoother has a much sharper frequency response — passes long cycles cleanly, kills short ones — while matching SMA / EMA at roughly the same lag.
• Critical period semantics. The period is the boundary, not a "length in bars" the way SMA's period is. SuperSmoother(10) passes a 20-bar cycle cleanly and attenuates a 5-bar cycle almost completely.

Common pitfalls

• Confusing period with SMA period. SuperSmoother(20) is much more aggressive than SMA(20) — it kills cycles shorter than ~10 bars entirely.
• Stacking unnecessarily. Ehlers warns against stacking multiple SuperSmoothers — they multiply lag without adding much attenuation.
• Period too short. period = 2 is degenerate (no real smoothing); the constructor enforces period > 1. Typical useful range is 5–30.

References

• John F. Ehlers, Cycle Analytics for Traders, Wiley (2013), ch. 3 — introduces SuperSmoother and the Roofing Filter family.

See also

• RoofingFilter — SuperSmoother + high-pass = cycle-band bandpass.
• Decycler — complementary trend extractor.
• Zlema — alternative low-lag smoother (not critically damped).
• Indicators-Overview — full taxonomy.