Time frequency analysis

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The approximation of a non-stationary signal by many locally stationary signals is something we might do in an analysis or synthesis procedure. One of the many places where uncertainty principles come into play. If we let the window size shrink to a single sample, then we are looking instead at empirical mode decompositions.

Chromatic derivatives, Welch-style DTFT spectrograms, wavelets sometimes. Wigner distribution (which is sort of a joint distribution over time and frequency). Constant Q transforms.

Much to learn here, even in the deterministic case.

I am especially interested in the Bayesian approach to this, a.k.a. probabilistic spectral analysis, which treats this as a problem in random functions.

TODO: In the classical setup we might still talk about distributions although these are usually Wigner distributions not probability distributions, which quantify something related to time-frequency uncertainty rather than posterior likelihoods. I would like to understand that.