Uncertainty and information in physiological signals: explicit physical trade-off with log-normal wavelets

Françoise Argoul (1) , Alexandre Guillet (1)

1 LOMA - Laboratoire Ondes et Matière d'Aquitaine

Physiological recordings contain a great deal of information about the underlying dynamics of life. The practical statistical treatment of these single-trial measurements is often hampered by the inadequacy of overly strong assumptions. Heisenberg's uncertainty principle allows for more parsimony, trading off statistical significance for localization. By decomposing signals into time-frequency atoms and recomposing them into local and flexible estimators, we propose a concise and expressive implementation of these fundamental concepts based on the choice of a geometric paradigm and two physical parameters. Starting from the spectrogram based on two fixed timescales and Gabor normal window, we then build its scale-invariant analogue, the scalogram based on two quality factors and Grossmann log-normal wavelet. These canonical estimators provide a minimal and flexible framework for single trial time-frequency statistics, which we apply to polysomnographic signals: EEG representations, coherence and mutual information between ECG-derived heart rate and respiration, and their spurious statistics.

Mots clés: Time-frequency analysis; Log-normal wavelet; Uncertainty principle; Polysomnography; Physiological signals; Coherence; Statistical significance; Mutual information; Single trial time-frequency statistics

Domaines: Physique [physics]; Physiologie [q-bio.TO]

Françoise Argoul, Alexandre Guillet. Uncertainty and information in physiological signals: explicit physical trade-off with log-normal wavelets. 2023. ⟨hal-04260114⟩