I think that you should aim at a decomposition level  that would comfortably yield the four bands and then keeping it constant try different wavelet basis. Decompose up till that level. Then reconstruct from the required coefficients and look at the error between the original signal and the reconstructed signal. Choose the basis which yields the smallest error.

You could also look at the cross-correlation between the wavelet and the EEG signal at different decomposition levels. The wavelet basis that yields the highest correlation at the required scales(those that represent the alpha, beta, gamma, etc) is the best basis for your application.

I faced the same challenge for an image processing task. the only solution I found , was to decompose image based on the weakest member of each family (for example 'db1') and compare the results. it does not seem to be a perfect solution, but looking at many research articles,this is what many researchers do!

@ Tannaz Akbarpour, it is a good method if you want to make the choices between the families but here I think you will also need the method to determine the exact member of the family that would satisfy the requirements of the problem.

A good strategy would be to look the model of the process that is under analysis and try to determine via the mathematical properties which wavelet is most suited or to use a decomposition method that is data driven like the Synchrosqueezing Wavelet transform, Empirical Wavelets etc. etc.    

thanks for your help, I will follow this strategy for my future tasks.

I just wonder, what is the reason to apply wavelets. Why not FT? Obviously, everything depends on the shape of the components. Since I do not know anything about them, so my comment is just for pointing at other, possibly better method. Certainly, if the componets are  sine-waves - the FT is a good tool. If they are rare pulses, additionally of different shapes (e.g. from  known classes), then the FT method  is  of low efficiency. If additionally, each part appears in its own time-interval, then the problem of extracting particular components is comparable to the method of reading words, isn't it?

Regards

@Joachim Domsta: 

Sir, the answer to your question is in it. The signals in the EEG are nonstationary, i.e. their distribution would vary with time. The basis functions of  FT are global in nature and thus are at a disadvantage when analyzing localized phenomena.

Moreover, the EEG is observed at the electrode after passing through the fluid in the skull, the skull and the brain itself. There is an overwhelming chance of dispersion and other nonlinear effects. Thus a localized decomposition of the EEG is beneficial as compared to a global FT.

Wavelets are a good choice as among the other prevalent methods they have a well defined mathematical theory which allows for analysis if one desires. The heuristic methods I am afraid would not allow such an analysis.

Regards, 

Zubair

Thank you, Joachim Domsta sir.

According to my knowledge,  For extracting the sub-bands from EEG signal there are many methods. Such as

FFT, STFT, FIR,WT (CWT & DWT) and digital filters.

EEG is a non-stationary signal. So FFT and STFT is not suitable.

CWT has another problem, that is the parameters what you used in CWT change time to time and unnecessary calculation required.

coming to DWT, it is good for non-stationary signals. But here the problem is finding a number of levels to decompose and selection of wavelet function.

@ Muhammad Zubair Ahmad, @ Venkata Phanikrishna Balam

I have upvoted both last answers  since they lead me closer to the problem. However, I am still curious about the general features of the sygnals analysed: What are the chararacteriscic features of particular "bands"? In particular:

What is a typical shape of, say, delta pulse/wave?

Can, say, alpha and beta pulses  appear simultaneously? Do they overlap?

What are their typical durations?

etc. etc Where can one read about typical outcome from the apparatus and how the doctors recognize particular elements?  Let me suggest already now, that  the shape of the mother wavelet should  be chosen  for each type of pulse separatley (probably this would be approprite if the signals of different type are separated in time, i.e. if their intervals of duration do not overlap). Therefore also in my first answer I have tried to compare the problem of words recognition, as another/additional way.

The recent examples of new techniques for the analysis of non stationary multi-scale signal include the Ramanujan sums method; an excellent introduction to the subject is discussed at

https://arxiv.org/pdf/0812.2170.pdf

I would like to strongly recommend this technique for investigation of the EEG signals. I do not see yet any publications on this subject but there is definitely an opportunity to make new contribution.

@Joachim Domsta

Sir, what you say is the best way to do so but unfortunately the reading of an EEG is a subject in itself. The EEG atlases which record wave forms of different types and their shapes are endless. Mostly the the difference between the Alpha, Beta, Gamma, Delta are based on their frequency.

Normally when recording an EEG the baselines are tested for every patient based on which waves dominate when eyes are open, eyes are closed etc. Sometimes medication can alter the normal pattern.

Thus the easier approach is adopted in the signal analysis community by just considering a filter bank approach and separating it out based on frequency.

I am not sure about the intervals of duration so I cannot comment on that. But if such were the case the word recognition would be a good example.

@ Muhammad Zubair Ahmad

Dear sir, thanks for your explanation. I am still interested in typical feature of particular signals.

Regards, Joachim

@Joachim Domsta

Sir, the following link may prove to be a useful introduction to the shape of the different brain waves.

Regards, 

Zubair

http://emedicine.medscape.com/article/1139332-overview#a1

@ Muhammad Zubair Ahmad

Dear sir, lot of thanks for the useful link. It is really interesting how can we recognize the waves from the output of EEG device!

Regards, Joachim

Check this.

https://elcvia.cvc.uab.es/article/view/v18-n1-sunkara