Time frequency analysis

Multiplying your exposure to uncertainty principles



🏗

The approximation of a non-stationary signal by many locally stationary signals.

Here I care more about the hack where you take a non-localised spectrogram and attempt to localise it over short windows of a long signal. That comes next.

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 which quantify something related to time-frequency uncertainty rather than posterior likelihoods. I would like to explain that.

References

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