What's the impact of a specific filter $\phi$ when building the wavelet scattering transform? I mean, if I compute the MFCC choosing different windows, (Hamming, Blackman, etc.), the behaviour concerning time-warping deformations changes. For instance, I got the best result (a pretty linear variation of the distance) with a Chebyshev window while other windows return a much faster increase of the distance with the deformation. I guess that it depends on the side lobes of the filter (it performs better where lobes are lower) but some ideas on this point would be appreciated.