Computational F-waves Extraction from Single-Lead Atrial Fibrillation ECG Based on a Frequency-Modulated Möbius Model

Atrial fibrillation (AF) is a prevalent arrhythmia characterized by the disappearance of P waves and the emergence of F waves in electrocardiogram (ECG) signals. F waves carry vital diagnostic information about AF episodes. This study proposes a computational method for extracting F waves from single-lead AF ECGs using a Frequency-Modulated Möbius (FMM) model. The algorithm decomposes AF signals into FMM-D components by adjusting a decomposition factor D, preserving the QRST wave phase information. These components are reconstructed to form QRST waves, and F waves are isolated through a template cancellation technique. Compared to Average Beat Subtraction (ABS) and Principal Component Analysis (PCA), the proposed method achieves lower normalized mean square error (NMSE), higher signal-to-component ratio (SC), and superior noise robustness. This approach provides a reliable computational framework for biomedical signal analysis and AF diagnosis.