EMD
EMD is an empirical and data-driven method developed to perform on non-stationary,non-linear, stochastic processes(it is ideally suitable for EEG signal analysis and processing)
Disadvantages:
1.the computational complexity is quite heavy(not suitable for online application)
2.the theory behind EMD is still not complete and so far used in empirical studies(difficult to predict its robustness in all EEG recordings)
EMD Algorithm
EMD algorithm decomposes a signal,s[n] into a sum of the band-limited components/functions,c[n] called intrinsic mode funciton(IMF) with well defined instantaneous frequencies.
Two Basic Conditions to be an IMF
1.the numberof extrema must be equal(or at most may differ by one) to the number of zero crossings
2.any point,the mean value of the two envelopes defined by the local maxima and the local minima has to be zero
The General Process flow of EMD Algorithm
Input: data sequence s[n]
1.Identify all the local extrema
2.Separately connect all the maxima and minima with natural cubic spline lines to form the upper,u[n],and lower,l[n],envelopes.
3.Find the mean of the envolopes as z[n]=[u[n]+l[n]]/2
4.Take the difference between the data and the mean as the proto-IMF,h[n]=s[n]-z[n]
5.Check the proto-IMF against the definition of IMF and the stoppage criterion to determine if it is an IMF
6.If the proto-IMF does not satisfy the definition,repeat step 1 to 5 on h[n] as many times as needed till it satisfies the definition
7.If the proto-IMF does satisfy the definition,assign the proto-IMF as an IMF component,c[n]
8.Repeat the operation step 1 to 7 on the residue,q[n]=s[n]-c[n],as the data
9.The operation ends when the residue contains no more than one extrema
EEMD(enhanced version of EMD)
EEMD it inspired from the fact that EMD is very sensitive to noise,which often leads to mode mixing complication.
EEMD is proposed which uses an average number of ensembles(IMFs) from EMD as the optimal IMFs thus it provides a noise-assisted data analysis method.