In EMD the basis is data driven. It is not fixed as in the wavelets or the Fourier Transform. The definition of an IMF does not make it mono-component  in the same sense as the Fourier modes. It is a band-pass component with frequencies lying in a small band. The idea is that is it really necessary to separate two nearby frequencies as two or consider them one component for practical purposes. This is the motivation behind the EMD. We can consider that the frequencies in the limited range are one component. This will make sense if you look at it from the perspective of hetrodyning. Non-linear effects cause the single frequency to disperse into nearby frequencies thus  making the response of a system a band rather than a single frequency.

If you look at envelop construction as is done in the AM transmission you will see that it requires low pass filtering. So when you perform iterative low pass filtering you will be left with the highest frequency component which satisfies the constraints on the number of zero crossings. This constraint is imposed in the algorithm.

Physically the EMD has been thought to model the system as a system of coupled oscillators, with each IMF representing the response of one of them.

I am attaching some publications below. I hope I make sense in the limited words that I have written.

http://ieeexplore.ieee.org/document/6655981/

Article One or Two Frequencies? The Empirical Mode Decomposition Answers

 Thank you, Zubair for your valuable response to my question.

Hi Zubair,

I have a doubt from your explanation that you said the idea is that is it really necessary to separate two nearby frequencies as two or consider them one component for practical purposes.  

So my doubt is here we are extracting a band of frequencies corresponding to a particular time instant and assuming them the instantaneous frequency at that time instant. - is it? 

From Huang-1998 paper, he had emphasized many times that in order to have a meaningful instantaneous frequency, the local restriction should be used in lieu of the global requirements given previously in other non-stationary data processing techniques. So here the local requirement is the finding the IMF from the local max, local mini, average of both and subtracting it from the original signal. 

Hi Arvind,

The IMF components as you would have noticed are Frequency Modulated, so they have a band of frequencies in them but can have a single instantaneous frequency.

An other experiment that you could do is to calculate the instanteous frequency of a multi-component signal. I think that it will be a single frequeqncy as is calculated by Huang but I am not sure.

Thanks Zubair

Hi Zubair,

I had one question as everywhere I found one sentence common for EMD decomposition that it adaptively and locally decomposes nonstationary time series data

into a sum of oscillatory modes, called Intrinsic mode functions (IMF).  

So here what is adaptively and locally with respect to physical sense and algorithm?

I will try to answer your question to the extent I understand it. hope it helps.

I am assuming that you want to know how the EMD algorithm decomposes the time series locally in an adaptive manner.

The answer to this lies in the method of interpolation and sampling of the data. Assuming sampling is not in our control. Mostly spline interpolation is used especially the cubic spline which uses three points thus bringing in the notion of locality. Moreover since we are constructing the envelops from the interpolation based on the samples and the IMFs are constructed by iterative low pass filtering, the IMFs are data dependent. Data dependent can also be called adaptive methods. You can find papers on the numerical experiments which investigate the dependence of EMD on sampling and interpolation methods.

http://perso.ens-lyon.fr/patrick.flandrin/NSIP03.pdf

Thanks a lot, Zubair bhai. Now I could get some insight of the EMD in term of physical sense.