Thanks. I think this is equivalent to applying a Hilbert transform to decompose a signal into AM/FM (or PM), but only getting the PM part.
We did a paper on that for DAFx a few years back

https://www.ntnu.edu/documents/1001201110/1266017954/DAFx-15_submission_30.pdf

========================
Prof. Victor Lazzarini
Maynooth University
Ireland

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