fmmpy : a Python module for frequency-modulated Möbius signal decomposition

We present fmmpy, an open-source Python library that implements the Frequency Modulated Möbius (FMM) model for robust decomposition of oscillatory signals into interpretable components. Beyond addressing the computational limitations of earlier implementations, fmmpy provides a significantly more flexible and general framework for applying the FMM model in diverse real-world scenarios. The package incorporates optimized algorithms and robust parameter constraint handling, showing how its improved flexibility and efficiency make it feasible to address problems that were previously too complex or slow to solve. This makes the FMM model more accessible and adaptable for diverse applications in biomedical, engineering, and other signal processing fields. To demonstrate its practical utility, we present two representative use cases: ECG analysis and signal spectrography, showing how the enhanced algorithms enable novel insights and solutions in these domains.