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Abstract

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.