I am trying to solve a problem very similar to the one discussed in this post
I have a broadband signal, which contains a component with time-varying frequency. I need to monitor the phase of this component over time. I am able to track the frequency shifts by (a somewhat brute force method of) peak tracking in the spectrogram. I need to "clean up" the signal around this time varying peak to extract the Hilbert phase (or, alternatively, I need a method of tracking the phase that does not involve the Hilbert transform).
To summarize that previous post: varying the coefficients of a FIR/IIR filter in time causes bad things to happen (it does not just shift the passband, it also completely confuses the filter state in ways that cause surprising transients). However, there probably is some way to adjust filter coefficients in time (probably by jointly modifying the filter coefficients and the filter state in some intelligent way). This is beyond my expertise, but I'd be open to any solutions.
There were two classes of solutions that seem plausible: one is to use a resonator filter (basically a damped harmonic oscillator driven by the signal) with a time-varying frequency. This model is simple enough to avoid surprising filter transients. I will try this -- but resonators have very poor attenuation in the stop band (if they can even be said to have a stop band?). This makes me nervous as I'm not 100% sure how the resonate filters will behave.
The other suggestion was to use a filter bank and smoothly interpolate between various band-pass filtered signals according to the frequency. This approach seems appealing, but I suspect it has some hidden caveats. I imagine that linearly mixing two band-pass filtered signals might not always do what you would expect, and might cause weird things? But, this is not my area of expertise, so if mixing over a filter bank is considered a safe solution (one that has been analyzed and published before), I would use it.
Another potential class of solutions occurs to me, which is to just take the phase from the frequency peak in a sliding short-time Fourier transform (could be windowed, multitaper, etc). If anyone knows any prior literature on this I'd be very interested. Related, would be to take the phase at the frequency power peak from a sliding complex Morlet wavelet transform over the band of interest.
So, I guess, basically I have three classes of solutions in mind. 1. Resonator filters with time-varying frequncy. 2. Using a filter bank, possibly with mixing? 3. Pulling phase from a STFT or CWT, (these can be considered a subset of the filter bank approach)
My supicion is that in (2,3) surprising thing will happen to the phase from time to time, and that in (1) we may not be able to reject as much noise as we'd like. It's not clear to me that this problem even has a perfect solution (uncertainty principle in time-frequency resolution?).
Anyway, if anyone has solved this before, and... even better, if anyone knows any papers that sound directly applicable here, I would be grateful.
Not sure if this will help, but googling "monitor phase of time varying component" resulted in this: Link
Hope that helps.