Which technique gives better result in extracting a band from a signal, let's say the alpha band (8-13 Hz): using a band-pass-filter or a DWT (Discrete Wavelet Transformation)?
P.S.: I am working in EEG processing.
With high probability, the band-pass filter.
DWT are invertible non-redundant discrete transformations that decompose data onto iterated low- and high-pass filters. Hence, the bands limits are mostly inverses of powers of two. So, you cannot chose arbitrary band values with DWT. More details can be found in the answer to What are the pros and cons of wavelet for filtering compared to conventional filters?
DWT satisfies additional properties (like perfect reconstruction, vanishing moments) that linear filters are not subject to. Hence, the choice in admissible DWT filters is reduced due to these additional constraints.
Hence, for pure band-pass filtering, a carefully designed pure band-filter can always be better than a DWT (and I usually am pro-wavelet). However, one can design a band-pass filter that is way worse than a DWT processing in certain settings.