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If a VMD analysis were fairly successful, in the sense that the spectrum is unimodal and relatively sparse, but still with a bit of bandwidth is it possible to extract a meaningful local amplitude and phase from it?

For instance, would it make sense to use the Hilbert transform of the output and use the usual magnitude and atan(imaginary/real) and unwrapping computations to obtain amplitude and phase?

Seems related to this post, Conditions for which the Hilbert transform returns a correct phase

Eli S
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  • Related – OverLordGoldDragon Feb 07 '23 at 10:22
  • @OverLordGoldDragon I agree. So it seems that if if each mode of VMD returns a single component (rather than bandlimited) frequency that amplitude will be recoverable with a Hilbert Transform. This is the case in my application, although it is not clear that the VMD spectral diagnostics identify some cases of failure. Are the conditions for phase essentially the same? – Eli S Feb 13 '23 at 17:39
  • I know nothing about VMD, but chances are very good it uses Hilbert implicitly or explicitly, like synchrosqueezing, CWT, and even STFT (as shown here, examples to be added). What I'd do is check all the steps involved in VMD and see if they involve operations with positive-only frequencies (e.g. filters with no negative freqs). -- Also in case you're not aware, synchrosqueezing can work great. – OverLordGoldDragon Feb 23 '23 at 11:37

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