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

TL;DR

ISAC addresses the need for a perceptually motivated, invertible audio front-end with controllable kernel sizes suitable for ML pipelines. It extends AUDlet by linearizing the auditory scale below a transition frequency $f^*$ to bound kernel lengths by $T_{ m max}$, while preserving perceptual bandwidth overlap. The approach yields a near-tight frame (κ ≈ 1) with stable reconstruction and enables learning a dual synthesis bank sharing the same kernel size, aided by a regularizer during training. Practically, ISAC enables efficient analysis-synthesis and mel-type spectrogram compression within ML models and is released as a PyTorch module in the HyBra package for seamless integration.

Abstract

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.

Figures (4)

• Figure 1: Frequency scales of ISAC filter banks for kernel sizes $256$, $128$, and $64$ (top to bottom), based on the ERB scale. The center frequencies in the dark area lie on a linear scale, and those in the light area on the ERB scale. The shorter the kernels, the larger the linear part of the scale becomes.
• Figure 2: Individual and total power spectral densities of an ISAC filter bank with $40$ kernels of size $T^*=128$. The flat total PSD indicates that the filter bank is well conditioned. The condition number for a decimation factor of $6$ is $\kappa = 1.05$.
• Figure 3: Individual and total power spectral densities of learned synthesis kernels for the setting of Fig. \ref{['fig:analysis']}. The reconstruction error is 6e-6. A regularizing term ensured that the total PSD stays flat. The condition number is $\kappa = 1.07$.
• Figure 4: Left: The compressed representation of a glitchy sound based on an ISAC filter bank ($K=40$, $T_{\max}=480$). Right: The mel spectrogram with the same settings. The output sizes match up to a few numbers of time bins.