What will be the interpretation of this principle with respect to these methods, have we bypassed it.
Here is a paper where they do Empirical Mode Decomposition (EMD) followed by a Gabor Transform.
http://www.ncbi.nlm.nih.gov/pubmed/24110584
Someone else combined the ideas behind wavelet decomposition (eg Gabor Transform) and EMD.
http://www.math.duke.edu/~jianfeng/paper/synsquez.pdf
You also might want to check this out:
http://dsp.stackexchange.com/questions/10660/understanding-bases-and-frames-for-gabor-transform
and finally
https://www.researchgate.net/publication/3343843_A_New_Formulation_for_Empirical_Mode_Decomposition_Based_on_Constrained_Optimization
Article A New Formulation for Empirical Mode Decomposition Based on ...
I am not sure if this is what you are asking, but there is indeed an uncertainty associated with Gabor's analytic signal and EMD, for that matter.
The problem that Gabor's analytic signal (and EMD as a sum of analytic signals) tries to solve is to reconstruct the time-dependent amplitude and frequency components of an Amplitude/Frequency modulated oscillator. That is, given x(t), you want to reconstruct A(t) and f(t) (you can think of frequency or phase interchangeably) such that
A(t) * sin(2pi * f(t) * t + phi0) = x(t)
Now, this problem is underdetermined, in the sense that several different pairs of will satisfy your single constraint, which is "match x(t)". So you need to provide further constraints to arrive at a unique solution. Further, it may be impossible to speak about _the_ amplitude or _the_ phase of the oscillator x(t), but only about your estimated values.
Hope that helps.
Cheers,
Fernando
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