Functional Data Analysis and Möbius Waves: Modeling and Inferential Advances for Oscillatory Signals

Y. Larriba, I. Fernández, C. Canedo Ortega, C. Rueda

The Frequency Modulated Möbius (FMM) approach is a flexible tool for analyzing oscillatory signals within the FDA framework. It provides a structured method for comprehending multidimensional synchronized signals. This approach decomposes signals into scaled Möbius waves, characterized by four parameters that capture location and shape variations, enabling precise estimation of oscillatory patterns.
We extend the FMM model by developing inferential procedures, based on likelihood estimation for non-linear models, for model parameters, signals and their derivatives. To do so, we employ classical estimation techniques to ensure accuracy and efficiency while analyzing asymptotic properties.
To validate our methodology, we conduct theoretical analysis and numerical experiments. Applied to electrocardiogram data and pattern-reversal visual evoked potentials, our approach highlights the practical advantages of the FMM paradigm and its potential applications in biomedical signal processing.

Keywords: Oscillatory Signals, FMM model, maximum likelihood estimation, ECG, pVEP

Functional data analysis II
June 12, 2025  11:30 AM
Sala VIP Jaume Morera i Galícia

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