Just want to call out the resources listed at the bottom of the Resonate website:

- The Oscillators app demonstrates real-time linear, log and Mel scale spectrograms, as well as derived audio features such as chromagrams and MFCCs https://alexandrefrancois.org/Oscillators/

- The Resonate Youtube playlist features video captures of real-time demonstrations. https://www.youtube.com/playlist?list=PLVcB_ABiKC_cbemxXUUJX...

- The open source Oscillators Swift package contains reference implementations in Swift and C++.https://github.com/alexandrefrancois/Oscillators

- The open source python module noFFT provides python and C++ implementations of Resonate functions and Jupyter notebooks illustrating their use in offline settings. https://github.com/alexandrefrancois/noFFT

Actually digging into SWIFT a bit more, the formulas differ by more than just the heuristic for alpha (unless I missed something) so the analysis in the SWIFT paper does not apply directly to(or maybe even at all).

yes - the sample app has demo of single resonator (so frequency bin equivalent) frequency estimation/tracking based on phase shift and also Doppler velocity computation (the code for these is in the Swift package, equations in the upcoming paper...). this video is from an older version of the demo app (less efficient implementation but same principle): https://www.youtube.com/watch?v=iQCPDJ8L_ao

Awesome - The code (Swift or C++) in the Oscillators package is probably the best place to look for implementation details https://github.com/alexandrefrancois/Oscillators

ping me if you have any question

At least I might have introduced a bit of creative noise in some AI coding models :-P