Decycler

John Ehlers' trend extractor — decycler = input - HighPass(input). Subtracts a 2-pole high-pass filter from the raw price, leaving the slow component: equivalent to a smoothed trend line with no group delay at low frequencies. The natural complement to SuperSmoother for cycle/trend decomposition.

Quick reference

Item	Value
Family	Ehlers / Cycle (DSP)
Input type	f64
Output type	f64
Output range	unbounded (price-units)
Default parameters	period is required (typical 20)
Warmup period	2 (uses input directly until recursion fills)
Interpretation	Trend line; no group delay at low frequencies

Formula

alpha = (cos(.707·2π/period) + sin(.707·2π/period) - 1) / cos(.707·2π/period)

HP_t = (1 - α/2)² · (x_t - 2·x_{t-1} + x_{t-2})
     + 2·(1 - α) · HP_{t-1}
     - (1 - α)² · HP_{t-2}

decycler_t = x_t - HP_t

The first two outputs simply equal the input (warmup buffering), the conventional Ehlers initialisation. See crates/wickra-core/src/indicators/decycler.rs.

Parameters

Name	Type	Default	Constraint	Description
period	usize	none	> 1	Critical period of the inner high-pass filter.

Decycler::new returns Error::PeriodZero for period == 0 and Error::InvalidPeriod for period == 1.

Inputs / Outputs

Indicator<Input = f64, Output = f64>. Python: Decycler(period).batch(prices) returns a 1-D np.ndarray (the first 2 bars pass through input unchanged). Node: same shape; update(value) returns number.

Warmup

warmup_period() == 2. The first two inputs pass through unchanged; from input 3 onward the proper high-pass recursion runs. By input ~2 · period the initial transient has decayed.

Edge cases

• Constant input. High-pass output decays to zero; decycler converges to the input.
• Step input. Critically damped — no overshoot. Roughly period bars to converge after a step.
• Pure cyclical input at exactly period. Filtered out almost entirely; decycler tracks the long-term level only.
• Reset. reset() clears the recursion state.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let prices: Vec<f64> = (0..100)
        .map(|i| {
            let trend = 100.0 + f64::from(i) * 0.5;
            let cycle = (f64::from(i) * 0.6).sin() * 5.0;
            trend + cycle
        })
        .collect();
    let mut dc = Decycler::new(20)?;
    let out = dc.batch(&prices);
    println!("row 50 decycler={:?}  raw={}", out[50], prices[50]);
    // decycler ≈ trend component only
    Ok(())
}

Python

import numpy as np
import wickra as ta

t = np.arange(100)
trend = 100 + t * 0.5
cycle = np.sin(t * 0.6) * 5
prices = trend + cycle
dc = ta.Decycler(20)
out = dc.batch(prices)
print('row 50:', out[50], 'vs trend:', trend[50])

Node

const wickra = require('wickra');
const dc = new wickra.Decycler(20);
const prices = Array.from({ length: 100 },
  (_, i) => 100 + i * 0.5 + Math.sin(i * 0.6) * 5);
console.log('row 50:', dc.batch(prices)[50]);

Streaming

use wickra::{Decycler, Indicator};

let mut dc = Decycler::new(20).unwrap();
let price_stream: Vec<f64> = Vec::new(); // your live price feed
for px in price_stream {
    let trend = dc.update(px).unwrap();
    // Use `trend` as the de-cycled price reference for slow-moving systems
}

Interpretation

• Trend line. Use Decycler as a low-lag trend reference — it matches an SMA at roughly the same period but with much less group delay at low frequencies.
• Vs SuperSmoother. They are duals: SuperSmoother is a lowpass (passes long cycles), Decycler is input − highpass (also passes long cycles, but with different phase response). SuperSmoother has tighter cutoff; Decycler has zero phase lag at DC.
• Pair with DecyclerOscillator. Subtracting a fast Decycler from a slow one gives the DecyclerOscillator, an MACD-like cycle-band indicator.

Common pitfalls

• Treating period as SMA period. The Decycler's critical period defines the boundary between trend and cycle, not the length of any averaging window. Decycler(20) is faster than SMA(20) in the trend regime.
• Expecting bounded output. Decycler tracks price scale; it's not an oscillator.
• Warmup misconception. The pass-through-input initial condition means the first 2 outputs equal the inputs — they look "correct" but carry no smoothing yet.

References

• John F. Ehlers, Cycle Analytics for Traders, Wiley (2013), ch. 4 — derives the Decycler from the high-pass complement.

See also

• DecyclerOscillator — MACD-like oscillator built on the Decycler difference.
• SuperSmoother — lowpass alternative.
• RoofingFilter — bandpass dual.
• Indicators-Overview — full taxonomy.