I have an EEG signal that I want to extract features to apply multilayer perceptron (MLP). What I should use, Fourier or wavelet coefficients?
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Fourier analysis doesn't provide you with temporal information. If you need temporal information you have several choices, two of which are the short term Fourier transform STFT, and wavelet transforms.
The STFT provides frequency coefficients in fixed time intervals across your data. There is a trade off between the time and frequency resolution obtained.
Wavelet transforms pick apart features in your data at various time resolutions which may give you better time localization for your coefficients. Additionally, you can choose different wavelet functions to control how features of your signal are extracted. Another way of saying this is that your choice of wavelet function affects what your coefficients represent.
Most of the work on feature extraction that I've seen recently (this is in general, no specific to EEG signals) employ some form of wavelet analysis.
Here is an example paper: http://uprt.vscht.cz/vav/RSoftware/S7help.pdf