  We propose a time-domain audio source separation method using down-sampling
(DS) and up-sampling (US) layers based on a discrete wavelet transform (DWT).
The proposed method is based on one of the state-of-the-art deep neural
networks, Wave-U-Net, which successively down-samples and up-samples feature
maps. We find that this architecture resembles that of multiresolution
analysis, and reveal that the DS layers of Wave-U-Net cause aliasing and may
discard information useful for the separation. Although the effects of these
problems may be reduced by training, to achieve a more reliable source
separation method, we should design DS layers capable of overcoming the
problems. With this belief, focusing on the fact that the DWT has an
anti-aliasing filter and the perfect reconstruction property, we design the
proposed layers. Experiments on music source separation show the efficacy of
the proposed method and the importance of simultaneously considering the
anti-aliasing filters and the perfect reconstruction property.
