Empirical Blaschke Mode decomposition: Algorithm and application

Abstract

Periodic pulse components are common in complex signals across fields like biomedical and aerospace engineering, and their accurate extraction is crucial for monitoring. We propose a novel method, Empirical Blaschke Mode Decomposition (EBMD), which uses the Blaschke Transform to capture quasi-periodic features and a unimodal pre-segmentation strategy to define relevant spectrum bands. A group sparse filter bank decomposes the signal into fundamental modes, extracting periodic pulse features. To prevent over-decomposition, a periodic frequency similarity fusion strategy consolidates the modes into eigenmode functions. EBMD is validated through simulations and applications in mechanical vibration feature extraction, EEG denoising, and ECG signal separation, demonstrating its ability to separate signals, extract features, and reduce noise.