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

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 quadratic estimates, 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’s normal window, we then build its scale-invariant analogue, the scalogram based on two quality factors and Grossmann’s 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, HRV extraction from ECG, coherence and mutual information between heart rate and respiration. • T-F decomposition of a signal into uncertainty atoms fixes one physical parameter. • T-F resolution and statistical significance controlled from a pair of quality factors. • Smoothing-based multitaper scalogram and spectrogram estimators applied to EEG. • Coherence significance relates to mutual information estimated in time and frequency. • Slow coherent modes in respiration and heart rate modulations of distinct phases.