ISAC: An Invertible and Stable Auditory Filter Bank with Customizable Kernels for ML Integration

This paper introduces ISAC, an invertible and stable, perceptually-motivated filter bank that is specifically designed to be integrated into machine learning paradigms. More precisely, the center frequencies and bandwidths of the filters are chosen to follow a non-linear, auditory frequency scale, the filter kernels have user-defined maximum temporal support and may serve as learnable convolutional kernels, and there exists a corresponding filter bank such that both form a perfect reconstruction pair. ISAC provides a powerful and user-friendly audio front-end suitable for any application, including analysis-synthesis schemes.

Grid-Based Decimation for Wavelet Transforms with Stably Invertible Implementation

The constant center frequency to bandwidth ratio (Q-factor) of wavelet transforms provides a very natural representation for audio data. However, invertible wavelet transforms have either required non-uniform decimation -- leading to irregular data structures that are cumbersome to work with -- or require excessively high oversampling with unacceptable computational overhead. Here, we present a novel decimation strategy for wavelet transforms that leads to stable representations with oversampling rates close to one and uniform decimation. Specifically, we show that finite implementations of the resulting representation are energy-preserving in the sense of frame theory. The obtained wavelet coefficients can be stored in a timefrequency matrix with a natural interpretation of columns as time frames and rows as frequency channels. This matrix structure immediately grants access to a large number of algorithms that are successfully used in time-frequency audio processing, but could not previously be used jointly with wavelet transforms. We demonstrate the application of our method in processing based on nonnegative matrix factorization, in onset detection, and in phaseless reconstruction.