Neural Analog Filter for Sampling-Frequency-Independent Convolutional Layer

A sampling-frequency-independent (SFI) convolutional layer is an extension of a convolutional layer to handle various sampling frequencies (SFs) with a single deep neural network (DNN). The SFI convolutional layer treats a standard convolutional layer as a collection of digital filters designed from analog filters. Analogous to the analog-to-digital filter conversion, it generates the weights from an SFI structure (latent analog filter) with respect to an input SF. To use the SFI layer, we need to define the mathematical forms of the latent analog filters before training. However, it is difficult to manually define the appropriate forms for an arbitrary network architecture. The inappropriate definition can result in the performance degradation. To overcome this problem, we propose a neural representation of analog filters, which can determine the forms of the latent analog filters in an end-to-end manner. The proposed method treats the latent analog filter as a function of continuous time or frequency and represents it using a DNN. Music source separation and speech separation experiments showed that the proposed method outperformed manually designed latent analog filters.