Empirical Mode Decomposition (EMD)

John Ehlers' adaptation of Empirical Mode Decomposition. Applies a bandpass centred on period, then detects peaks and valleys over a fraction of the period, averages them into upper / lower envelopes, and returns the centred bandpass minus the envelope mean. The result crosses zero at trend changes and stays near zero in non-trending markets — the classic visual cue Ehlers documents.

Quick reference

Item	Value
Family	Ehlers / Cycle (DSP)
Input type	f64
Output type	f64
Output range	unbounded; centred near zero
Default parameters	period, fraction required (Ehlers' typical (20, 0.5))
Warmup period	period
Interpretation	Near-zero → no trend; persistently positive/negative → trend

Formula

1. Bandpass, centred at period:

   β   = cos(2π / period)
   γ   = 1 / cos(4π · 0.1 / period)         (using fraction-derived term)
   α   = γ - sqrt(γ² - 1)
   BP_t = 0.5 · (1 - α) · (x_t - x_{t-2})
        + β · (1 + α) · BP_{t-1}
        - α · BP_{t-2}

2. Peak / valley detection over a fraction · period window of the bandpass output: a local maximum becomes a "peak", a local minimum becomes a "valley".

3. Envelope smoothing: peaks and valleys are each fed into a SuperSmoother to form upper / lower envelopes.

4. Output:

   EMD_t = BP_t - (upper_env_t + lower_env_t) / 2

See crates/wickra-core/src/indicators/empirical_mode_decomposition.rs.

Parameters

Name	Type	Default	Constraint	Description
period	usize	none	> 1	Bandpass centre period.
fraction	f64	none	finite, (0, 1]	Fraction of period used for peak/valley window.

EmpiricalModeDecomposition::new returns Error::PeriodZero for period == 0, Error::InvalidPeriod for period == 1, and an appropriate error for invalid fraction.

Inputs / Outputs

Indicator<Input = f64, Output = f64>. Python: EmpiricalModeDecomposition(period, fraction).batch(prices) returns a 1-D np.ndarray with NaN in the warmup prefix. Node: same shape; update(value) returns number | null.

Warmup

warmup_period() ≈ period. The bandpass and peak/valley smoothers need a full period each before the output stabilises.

Edge cases

• Constant input. Bandpass output is zero; envelopes both zero; EMD output is zero.
• Strong trend. Bandpass output drifts away from zero; envelope means lag behind, so EMD reads consistently positive (uptrend) or negative (downtrend).
• fraction too small. Peak/valley windows too narrow; the envelope tracks every wiggle and EMD becomes noisy.
• Reset. reset() clears all internal buffers and the inner SuperSmoothers.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let prices: Vec<f64> = (0..200)
        .map(|i| 100.0 + (f64::from(i) * 0.3).sin() * 5.0 + f64::from(i) * 0.05)
        .collect();
    let mut emd = EmpiricalModeDecomposition::new(20, 0.5)?;
    println!("row 100 = {:?}", emd.batch(&prices)[100]);
    Ok(())
}

Python

import numpy as np
import wickra as ta

t = np.arange(200)
prices = 100 + np.sin(t * 0.3) * 5 + t * 0.05  # cycle + drift
emd = ta.EmpiricalModeDecomposition(20, 0.5)
print('row 100:', emd.batch(prices)[100])  # positive = uptrend

Node

const wickra = require('wickra');
const emd = new wickra.EmpiricalModeDecomposition(20, 0.5);
const prices = Array.from({ length: 200 },
  (_, i) => 100 + Math.sin(i * 0.3) * 5 + i * 0.05);
console.log('row 100:', emd.batch(prices)[100]);

Streaming

use wickra::{EmpiricalModeDecomposition, Indicator};

let mut emd = EmpiricalModeDecomposition::new(20, 0.5).unwrap();
let price_stream: Vec<f64> = Vec::new(); // your live price feed
for px in price_stream {
    if let Some(v) = emd.update(px) {
        let regime = if v.abs() < 0.5 { "cycle" } else if v > 0.0 { "uptrend" } else { "downtrend" };
        println!("EMD={v:.3}  regime={regime}");
    }
}

Interpretation

• Trend regime classifier. Near-zero output = the market is cycling around the bandpass centre; persistently non-zero output = there's a trend component the cycle filter can't capture.
• Direction. Positive output indicates the cycle is centred above the envelope mid-line (uptrend bias); negative for downtrend.
• Pair with cycle oscillators. EMD acts as a trend filter; pair it with CenterOfGravity or RSI for entries — only trade when EMD says trend matches your setup.

Common pitfalls

• Treating EMD as a momentum indicator. It's a trend regime classifier, not a momentum reading. The magnitude reflects trend strength, not bar-to-bar momentum.
• fraction tuning. 0.5 is the Ehlers default. Smaller values (0.25) catch more peaks but are noisier; larger (0.75) catch fewer but are smoother.
• Warmup ignored. First ~period bars are unreliable; gate signals to bars past the warmup explicitly.

References

• John F. Ehlers, Cycle Analytics for Traders, Wiley (2013), ch. 14 — Ehlers' adaptation of the original Huang et al. EMD.
• N.E. Huang et al., The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. Royal Society A, 1998 — original EMD derivation.

See also

• RoofingFilter — alternative band-isolation tool.
• SuperSmoother — building block for the envelope smoothers.
• DecyclerOscillator — different trend-vs-cycle decomposition.
• Indicators-Overview — full taxonomy.