Download Physical Modeling Using Recurrent Neural Networks with Fast Convolutional Layers Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or partial differential equations, using established techniques. Recent work has applied the techniques of machine-learning to construct such models automatically from data for the case of systems which have lumped states described by scalar values, such as electrical circuits. In this work, we examine how similar techniques are able to construct models of systems which have spatially distributed rather than lumped states. We describe several novel recurrent neural network structures, and show how they can be thought of as an extension of modal techniques. As a proof of concept, we generate synthetic data for three physical systems and show that the proposed network structures can be trained with this data to reproduce the behavior of these systems.
Download Differentiable White-Box Virtual Analog Modeling Component-wise circuit modeling, also known as “white-box”
modeling, is a well established and much discussed technique in
virtual analog modeling. This approach is generally limited in accuracy by lack of access to the exact component values present in
a real example of the circuit. In this paper we show how this problem can be addressed by implementing the white-box model in a
differentiable form, and allowing approximate component values
to be learned from raw input–output audio measured from a real
device.
Download Generalizing Root Variable Choice in Wave Digital Filters with Grouped Nonlinearities Previous grouped-nonlinearity formulations for Wave Digital Filter (WDF) modeling of nonlinear audio circuits assumed that nonlinear (NL) devices with memoryless voltage–current characteristics were modeled as voltage-controlled current sources (VCCSs). These formulations cannot accommodate nonlinear devices whose equations cannot be written as NL VCCSs, and they cannot accommodate circuits with cutsets composed entirely of current sources (including NL VCCSs). In this paper we generalize independent and dependent variable choice at the root of WDF trees to accommodate both these cases, and review two graph theorems for avoiding forbidden cutsets and loops in general.
Download WDF Modeling of a Korg MS-50 Based Non-linear Diode Bridge VCF The voltage-controlled low-pass filter of the Korg MS-50 synthesizer is built around a non-linear diode bridge as the cutoff frequency control element, which greatly contributes to the sound of this vintage synthesizer. In this paper, we introduce the overall filter circuitry and give an in-depth analysis of this diode bridge. It is further shown how to turn the small signal equivalence circuit of the bridge into the necessary two-resistor configuration to uncover the underlying Sallen-Key structure. In a second step, recent advances in the field of WDFs are used to turn a simplified version of the circuit into a virtual-analog model. This model is then examined both in the small-signal linear domain as well as in the non-linear region with inputs of different amplitudes and frequencies to characterize the behavior of such diode bridges as cutoff frequency control elements.
Download Reducing the Aliasing of Nonlinear Waveshaping Using Continuous-Time Convolution Nonlinear waveshaping is a common technique in musical signal processing, both in a static memoryless context and within feedback systems. Such waveshaping is usually applied directly to a sampled signal, generating harmonics that exceed the Nyquist frequency and cause aliasing distortion. This problem is traditionally tackled by oversampling the system. In this paper, we present a novel method for reducing this aliasing by constructing a continuous-time approximation of the discrete-time signal, applying the nonlinearity to it, and filtering in continuous-time using analytically applied convolution. The presented technique markedly reduces aliasing distortion, especially in combination with low order oversampling. The approach is also extended to allow it to be used within a feedback system.
Download On the Equivalence of Integrator- and Differentiator-Based Continuous- and Discrete-Time Systems The article performs a generic comparison of integrator- and differentiator based continuous-time systems as well as their discretetime models, aiming to answer the reoccurring question in the
music DSP community of whether there are any benefits in using differentiators instead of conventionally employed integrators.
It is found that both kinds of models are practically equivalent, but
there are certain reservations about differentiator based models.