Differentiable Modelling of Percussive Audio with Transient and Spectral Synthesis

Differentiable digital signal processing (DDSP) techniques, including methods for audio synthesis, have gained attention in recent years and lend themselves to interpretability in the parameter space. However, current differentiable synthesis methods have not explicitly sought to model the transient portion of signals, which is important for percussive sounds. In this work, we present a unified synthesis framework aiming to address transient generation and percussive synthesis within a DDSP framework. To this end, we propose a model for percussive synthesis that builds on sinusoidal modeling synthesis and incorporates a modulated temporal convolutional network for transient generation. We use a modified sinusoidal peak picking algorithm to generate time-varying non-harmonic sinusoids and pair it with differentiable noise and transient encoders that are jointly trained to reconstruct drumset sounds. We compute a set of reconstruction metrics using a large dataset of acoustic and electronic percussion samples that show that our method leads to improved onset signal reconstruction for membranophone percussion instruments.Comment: To be published in The Proceedings of Forum Acusticum, Sep 2023, Turin, Ital

Differentiable Modelling of Percussive Audio with Transient and Spectral Synthesis

Differentiable digital signal processing (DDSP) techniques, including methods for audio synthesis, have gained attention in recent years and lend themselves to interpretability in the parameter space. However, current differentiable synthesis methods have not explicitly sought to model the transient portion of signals, which is important for percussive sounds. In this work, we present a unified synthesis framework aiming to address transient generation and percussive synthesis within a DDSP framework. To this end, we propose a model for percussive synthesis that builds on sinusoidal modeling synthesis and incorporates a modulated temporal convolutional network for transient generation. We use a modified sinusoidal peak picking algorithm to generate time-varying non-harmonic sinusoids and pair it with differentiable noise and transient encoders that are jointly trained to reconstruct drumset sounds. We compute a set of reconstruction metrics using a large dataset of acoustic and electronic percussion samples that show that our method leads to improved onset signal reconstruction for membranophone percussion instruments

Complex Neural Networks for Audio

Audio is represented in two mathematically equivalent ways: the real-valued time domain (i.e., waveform) and the complex-valued frequency domain (i.e., spectrum). There are advantages to the frequency-domain representation, e.g., the human auditory system is known to process sound in the frequency-domain. Furthermore, linear time-invariant systems are convolved with sources in the time-domain, whereas they may be factorized in the frequency-domain. Neural networks have become rather useful when applied to audio tasks such as machine listening and audio synthesis, which are related by their dependencies on high quality acoustic models. They ideally encapsulate fine-scale temporal structure, such as that encoded in the phase of frequency-domain audio, yet there are no authoritative deep learning methods for complex audio. This manuscript is dedicated to addressing the shortcoming. Chapter 2 motivates complex networks by their affinity with complex-domain audio, while Chapter 3 contributes methods for building and optimizing complex networks. We show that the naive implementation of Adam optimization is incorrect for complex random variables and show that selection of input and output representation has a significant impact on the performance of a complex network. Experimental results with novel complex neural architectures are provided in the second half of this manuscript. Chapter 4 introduces a complex model for binaural audio source localization. We show that, like humans, the complex model can generalize to different anatomical filters, which is important in the context of machine listening. The complex model\u27s performance is better than that of the real-valued models, as well as real- and complex-valued baselines. Chapter 5 proposes a two-stage method for speech enhancement. In the first stage, a complex-valued stochastic autoencoder projects complex vectors to a discrete space. In the second stage, long-term temporal dependencies are modeled in the discrete space. The autoencoder raises the performance ceiling for state of the art speech enhancement, but the dynamic enhancement model does not outperform other baselines. We discuss areas for improvement and note that the complex Adam optimizer improves training convergence over the naive implementation

A sinusoidal signal reconstruction method for the inversion of the mel-spectrogram

The synthesis of sound via deep learning methods has recently received much attention. Some problems for deep learning approaches to sound synthesis relate to the amount of data needed to specify an audio signal and the necessity of preserving both the long and short time coherence of the synthesised signal. Visual time-frequency representations such as the log-mel-spectrogram have gained in popularity. The log- mel-spectrogram is a perceptually informed representation of audio that greatly compresses the amount of information required for the description of the sound. However, because of this compression, this representation is not directly invertible. Both signal processing and machine learning techniques have previ- ously been applied to the inversion of the log-mel-spectrogram but they both caused audible distortions in the synthesised sounds due to issues of temporal and spectral coherence. In this paper, we outline the application of a sinusoidal model to the ‘inversion’ of the log-mel-spectrogram for pitched musical instrument sounds outperforming state-of-the-art deep learning methods. The approach could be later used as a general decoding step from spectral to time intervals in neural applications