Residual Hybrid Filterbanks

A hybrid filterbanks is a convolutional neural network (convnet) whose learnable filters operate over the subbands of a non-learnable filterbank, which is designed from domain knowledge. While hybrid filterbanks have found successful applications in speech enhancement, our paper shows that they remain susceptible to large deviations of the energy response due to randomness of convnet weights at initialization. Against this issue, we propose a variant of hybrid filterbanks, by inspiration from residual neural networks (ResNets). The key idea is to introduce a shortcut connection at the output of each non-learnable filter, bypassing the convnet. We prove that the shortcut connection in a residual hybrid filterbank lowers the relative standard deviation of the energy response while the pairwise cosine distances between non-learnable filters contributes to preventing duplicate features.