Signal processing
Empirical Mode Decomposition (EMD) for PPG Processing
Empirical Mode Decomposition (EMD) is a data-adaptive signal decomposition method that decomposes a PPG signal into a finite set of Intrinsic Mode Functions (IMFs) through an iterative sifting process, without requiring predefined basis functions. Each IMF represents a natural oscillation mode of the signal, enabling adaptive separation of cardiac, respiratory, and motion artifact components.
How it works
Schematic summary of this guide. Waveforms are illustrative, not measured data.
The EMD sifting algorithm identifies local maxima and minima of the signal, constructs upper and lower envelopes by cubic spline interpolation, computes the mean envelope, and subtracts it from the signal to produce a candidate IMF. This process iterates until the candidate satisfies the IMF criteria (≤ one extrema-zero crossing discrepancy). The procedure repeats on the residual to extract successive IMFs until the residual is monotonic.
For PPG, the first 2–4 IMFs typically contain high-frequency noise and motion artifacts, while IMFs 3–6 capture the cardiac oscillation band (0.5–3 Hz). The remaining IMFs encode respiratory modulation (0.15–0.4 Hz), baseline drift, and DC offset. Identifying the cardiac IMFs is typically done by computing the cross-correlation of each IMF with a clean PPG template or by selecting IMFs with dominant frequency closest to the expected heart rate.
Ensemble EMD (EEMD) and Complete EEMD with Adaptive Noise (CEEMDAN) address mode mixing — a fundamental limitation of standard EMD where a single IMF contains oscillations from multiple frequency bands.
Frequently Asked Questions
How does EMD handle non-stationary PPG signals?
EMD is fully adaptive and data-driven — it imposes no stationarity or linearity assumptions. Each IMF is locally stationary, allowing EMD to handle PPG non-stationarities (heart rate changes, motion artifacts, vasoconstriction) that violate wavelet or Fourier assumptions.
What is the Hilbert-Huang Transform (HHT) in the context of PPG?
HHT applies the Hilbert Transform to each IMF to compute instantaneous frequency and amplitude. For PPG cardiac IMFs, Hilbert-derived instantaneous frequency provides beat-to-beat heart rate with higher temporal resolution than FFT-based methods.
Is EMD suitable for real-time wearable PPG processing?
Standard EMD is iterative and computationally intensive, making it challenging for real-time edge processing.