EMD

Ehlers DSP decomposition cycle spectral dsp

Empirical Mode Decomposition separates cycles from trends using bandpass filtering and identifies market modes via adaptive thresholds.

Visual Example

EMD — annotated preview mapping to core implementation

Synthetic ideal per library logic. Generated 2026-07-01 IST via docs/generate_all_previews.py (reproducible; maps to core Next<T> implementation).

Description

Empirical Mode Decomposition separates cycles from trends using bandpass filtering and identifies market modes via adaptive thresholds.

Use to decompose price into Intrinsic Mode Functions to separate cycles of different periods without any a priori period assumption. Useful for multi-timescale analysis.

Part of QuantWave's Ehlers digital signal processing suite. Designed for low-lag cycle and trend work — pair with Roofing Filter or SuperSmoother on noisy inputs.

Empirical Mode Decomposition is a data-driven method developed by Huang et al. (1998) that decomposes a signal into Intrinsic Mode Functions by iteratively sifting local extrema. Unlike Fourier methods, it requires no predetermined basis functions, making it adaptive to non-stationary market data.

Typical applications:

Use for cycle timing in mean-reverting regimes
Gate with Hurst exponent or ADX before taking cycle signals
Allow 20+ bars warm-up for filter state to stabilise
Chain with Roofing Filter when input is noisy

QuantWave implements this via the universal Next<T> trait — bit-identical across Rust streaming, Python streaming, and Polars .ta() batch plugins.

Formula / Specification

Implementation (quantwave-core/src/indicators/emd.rs):

[ \beta = \cos\left(\frac{360}{P}\right), \gamma = \frac{1}{\cos\left(\frac{720\delta}{P}\right)}, \alpha = \gamma - \sqrt{\gamma^2 - 1} ] [ BP = 0.5(1 - \alpha)(Price - Price_{t-2}) + \beta(1 + \alpha)BP_{t-1} - \alpha BP_{t-2} ] [ Mean = \text{SMA}(BP, 2P) ] [ Threshold = \text{Fraction} \cdot \text{SMA}(\text{Peak/Valley}, 50) ]

Gold-standard parity vectors: quantwave-core/tests/gold_standard/emd.json.

Parameters

Parameter	Default	Description
`period`	20	Bandpass center period
`delta`	0.5	Bandwidth half-width
`fraction`	0.1	Threshold multiplier for peaks/valleys

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::EMD;
use quantwave_core::traits::Next;

let mut ind = EMD::new(20);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import EMD

ind = EMD(20)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_emd(series: pl.Series) -> pl.Series:
    ind = qw.EMD(20)
    return pl.Series([ind.next(float(v)) for v in series.to_list()])

df = (
    pl.read_csv('ohlcv.csv')
    .lazy()
    .with_columns(
        pl.col("close").map_batches(apply_emd, return_dtype=pl.Float64).alias("emd")
    )
    .collect()
)

All surfaces are bit-identical via the single Next<T> implementation and proptests.

Edge Cases & Limitations

Recursive DSP filters require a warm-up period; first N bars may be unstable or raw-pass-through.
Designed for cyclic/mean-reverting regimes; trending markets can produce lag or drift.
Parameter period (or equivalent) controls cutoff — too small adds noise, too large adds lag.
Prefer chaining with other Ehlers tools (Roofing Filter, SuperSmoother) on noisy inputs.
Validated via proptests against gold-standard vectors where available.
No look-ahead bias; suitable for live streaming and batch feature pipelines.

Boundary Behavior

Condition	Behavior
Warm-up	Leading bars return NaN until warmup_bars is satisfied.
period > len	When period exceeds series length, output is all NaN.
NaN inputs	NaN in input propagates to output (NaN out).
Invalid params	Non-positive period or missing required params raise ValueError.
Empty data	Empty input returns an empty result series.

Sources & References

Primary Source: https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/EmpiricalModeDecomposition.pdf

Implementation: quantwave-core/src/indicators/emd.rs (EMD / EMD_METADATA). Parity: quantwave-core/tests/gold_standard/emd.json

Provenance: Standards bulk upgrade 2026-07-01 IST — see docs/DOCUMENTATION_STANDARDS.md.

EMD