Curious if there is available math to show the gain scale properties of this technique across the spectrum -- in other words its frequency response. The system doesn't appear to be LTI so I don't believe we can utilize the Z-transform to do this. Phase response would also be important as well.
The Sliding Windowed Infinite Fourier Transform (SWIFT) has very similar math, and they provide some analysis in the paper. I use a different heuristic for alpha so I am not sure the analysis transfers directly. In my upcoming paper I have some numerical experiments and graphs that show resonator response across the range.
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).