Investigation on Wavelet Basis Function of DNN-based Time Domain Audio Source Separation Inspired by Multiresolution Analysis

We address time-domain audio source separation based on deep neural networks (DNNs) inspired by multiresolution analysis, which we call multiresolution deep layered analysis (MRDLA). Time-domain audio source separation estimates individual sources from an observed mixture signal in an end-to-end manner. The MRDLA model successively downsamples feature maps with down-sampling (DS) layers based on a discrete wavelet transform (DWT), which we call the DWT layers. Using the DWT layers can solve the underlying problems of one of conventional time-domain DNNs, Wave-U-Net: Since the DS layers of Wave-U-Net decimate the feature maps with no preceding low-pass filters, they cause aliasing and discard part of the feature maps; In contrast, the DWT layers have anti-aliasing filters and preserve the entire information of the feature maps, which can improve the separation performance. The architecture of the DWT layers allows for changing the frequency responses by choosing the wavelet basis functions. In this paper, since not only the existence but also the frequency responses of the anti-aliasing filters may affect the separation performance, we conduct an empirical study of the wavelet basis functions to discuss their effect for the separation performance.