Show HN: Resonate – real-time high temporal resolution spectral analysis

Re:Show HN: Resonate – real-time high temporal resolution sp... by waffletower on Tuesday April 15, 2025 @02:21PM (#43696587)

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.

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Re:Show HN: Resonate – real-time high temporal resolution sp... by arjf on Wednesday April 16, 2025 @10:56AM (#43706372)

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.

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Re:Show HN: Resonate – real-time high temporal resolution sp... by arjf on Thursday April 17, 2025 @12:04PM (#43718773)

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).

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