I have been studying the Hilbert-Huang transform, which I understand is a frequency analysis technique that uses the adaptive IMFs basis components to decompose a signal using EMD.
I understand that frequency analysis techniques such as the STFT (short-time Fourier transform) and Wavelet transform involve the convolution of a signal with a predefined basis in order to extract frequency information.
Several articles from Huang and others state "convolution processes involve integration, which makes the results suffering the limitation imposed by the uncertainty principle".
I also understand that the frequency of each IMF is extracted by finding the time rate of change of phase of the analytic signal for each IMF (which would involve differentiation of the phase with respect to time).
Why does this differentiation mean that the uncertainty principle is avoided?
I have a vague idea that it's due to operators associated with time and frequency that don't commute, but I have struggled to find any sources that approach this from a signal processing/mathematical perceptive rather than in a quantum mechanical sense.
Furthermore, if this kind of signal processing circumvents the uncertainty principle, does that mean time and frequency events can be resolved with arbitrary precision?
(In my head, this, in turn, would have implications in quantum mechanics, but I imagine this would be outside the topic of this site.)
Any insights and/or articles are gratefully received.