Frequency Modulated Möbius as an Extension of Fourier Decomposition

C. Canedo Ortega, R. Carratalá Sáez, C. Rueda Sabater

The analysis of oscillatory signals is essential in various fields, particularly in medicine, where the electrocardiogram (ECG) is a key diagnostic tool. A crucial step in automatic processing is the decomposition of signals into meaningful components. This work explores the relationship between two decomposition methods for multi-channel signals: Adaptive Fourier Decomposition (AFD) and Frequency Modulated Möbius (FMM).

We establish the equivalence between AFD and FMM for finite-order decompositions and show that, under general conditions, their estimation procedures lead to the same optimization problem. AFD offers greater computational efficiency, while FMM provides better interpretability, making it useful for tasks like pattern recognition. We present numerical experiments that further validate these findings, demonstrating how combining both approaches enhances their applicability in signal processing.

Keywords: Frequency-Modulated Möbius, Fourier Decomposition, Signal Analysis

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