Paper Archive

The design of Virtual Analog (VA) algorithms has traditionally been divided between white-box (physics-based) and black-box (data-driven) approaches. Recent work has shown that hybrid methods, combining physical modeling with neural networks, can effectively leverage the strengths of both paradigms. In particular, Wave Digital Filters (WDFs) can be coupled with Multi-Layer Perceptrons (MLPs) to model circuits with multiple nonlinearities in a fully explicit manner. In this paper, we present a comparative study investigating the use of Kolmogorov-Arnold Networks (KANs) for VA modeling within the WDF framework. Unlike MLPs, KANs shift the learning paradigm by parameterizing activation functions instead of relying exclusively on learned weight matrices, potentially enabling more compact representations. Results show that, for our case study, KANs achieve accuracy comparable to MLPs while requiring approximately 70% fewer parameters at the cost of increased computational complexity. These findings suggest that KANs may represent a promising alternative in scenarios where memory footprint is a primary constraint, such as embedded audio applications, or when target models feature numerous nonlinear elements.

Download

We present our submission to Task A of the 1st DAFx Parameter Estimation Challenge, which concerns the estimation of the physical parameters of a vibrating plate from a synthetic impulse response. Our approach introduces a differentiable modal plate synthesizer and estimates the plate parameters through inference-time gradient-based optimization of the synthesizer parameters. The six target parameters are recovered by minimizing a multi-scale spectral loss via backpropagation through the differentiable plate model. To handle the non-convexity of the loss landscape, we adopt a two-phase training strategy consisting of multiple short-term probe optimizations, followed by full-scale refinement initialized from the best candidate. We evaluate the approach on eight impulse responses synthesized with the official challenge dataset generator. Compared with a constant-value predictor and the particle swarm optimization baseline provided by the challenge, the proposed method reduces the prediction error by approximately one order of magnitude.

Download

Modeling violin bridge admittance is a long-standing problem in musical acoustics, with applications in sound analysis, synthesis, and virtual instrument design. In this work, we investigate the use of the Eigensystem Realization Algorithm (ERA) for deriving reduced-order state-space models directly from measured impulse responses. The proposed approach allows us to extract dominant system dynamics and obtain compact realizations without requiring explicit modal parameterization. We evaluate ERA on a dataset of modern and historical violins and compare it against established modal and state-space identification methods. Experimental results demonstrate that ERA outperforms existing approaches by achieving lower reconstruction errors in both the time and frequency domains while preserving perceptually relevant characteristics of the bridge response. Furthermore, we show that the state-space realizations obtained using ERA reproduce the target frequency-dependent energy decay more accurately than models obtained using the baseline methods. These findings support the use of ERA as an efficient and flexible alternative for modeling violin bridge admittances, with applications that span from audio synthesis and processing to instrument virtualization.

Download

Virtual Analog (VA) modeling is the practice of digitally emulating analog audio gear. Over the past few years, with the purpose of recreating the alleged distinctive sound of audio equipment and musicians, many different guitar pedals have been emulated by means of the VA paradigm but little attention has been given to phasers. Phasers process the spectrum of the input signal with time-varying notches by means of shifting stages typically realized with a network of transistors, whose nonlinear equations are, in general, demanding to be solved. In this paper, we take as a reference the famous MXR Phase 90 guitar pedal, and we propose an efficient time-varying model of its Junction Field-Effect Transistors (JFETs) based on a channel resistance approximation. We then employ such a model in the Wave Digital domain to emulate in real-time the guitar pedal, obtaining an implementation characterized by low computational cost and good accuracy.

Download

Neural networks have been applied within the Wave Digital Filter (WDF) framework as data-driven models for nonlinear multi-port circuit elements. Conventionally, these models are trained on wave variables obtained by sampling the current-voltage characteristic of the considered nonlinear element before being incorporated into the circuit WDF implementation. However, isolating multi-port elements for this process can be challenging, as their nonlinear behavior often depends on dynamic effects that emerge from interactions with the surrounding circuit. In this paper, we propose a novel approach for training neural models of nonlinear multi-port elements directly within a circuit’s Wave Digital (WD) discretetime implementation, relying solely on circuit input-output voltage measurements. Exploiting the differentiability of WD simulations, we embed the neural network into the simulation process and optimize its parameters using gradient-based methods by minimizing a loss function defined over the circuit output voltage. Experimental results demonstrate the effectiveness of the proposed approach in accurately capturing the nonlinear circuit behavior, while preserving the interpretability and modularity of WDFs.

Download

Neural networks that operate directly on time-domain signals are widely used for virtual analog (VA) modeling. A key limitation of these models is their dependence on the sampling rate used during training, which becomes implicitly encoded in the learned parameters, so that changing it generally alters the realized dynamics. Although architectural modifications to recurrent neural networks have been proposed to enable sample-rate independent operation, these approaches are inherently tailored to upsampling and do not accommodate downsampling scenarios. In this manuscript, we present a VA modeling framework based on Fourier Neural Operators (FNOs) adapted to process fixed-duration audio frames. The proposed formulation defines the learned mapping over a fixed temporal support and evaluates it on uniform grids of different densities, so that a model trained at a single sampling rate can be applied at unseen sampling resolutions. Numerical results on a nonlinear transistor circuit show that the proposed model achieves competitive accuracy in upsampling scenarios while remaining directly applicable to downsampling, unlike a sample-rate independent baseline recurrent architecture.

Download

Scattering delay networks (SDNs) provide a flexible and efficient framework for artificial reverberation and room acoustic modeling. In this work, we introduce a differentiable SDN, enabling gradient-based optimization of its parameters to better approximate the acoustics of real-world environments. By formulating key parameters such as scattering matrices and absorption filters as differentiable functions, we employ gradient descent to optimize an SDN based on a target room impulse response. Our approach minimizes discrepancies in perceptually relevant acoustic features, such as energy decay and frequency-dependent reverberation times. Experimental results demonstrate that the learned SDN configurations significantly improve the accuracy of synthetic reverberation, highlighting the potential of data-driven room acoustic modeling.

Download

Several digital signal processing approaches, generally referred to as Virtual Analog (VA) modeling, are currently under development for the software emulation of analog audio circuitry. The main purpose of VA modeling is to faithfully reproduce the behavior of real-world audio gear, e.g., distortion effects, synthesizers or amplifiers, using efficient algorithms. In this paper, however, we provide a preliminary discussion about how VA modeling can be exploited to infer the input signal of an analog audio system, given the output signal and the parameters of the circuit. In particular, we show how an inversion theorem known in circuit theory, and based on nullors, can be used for this purpose. As recent advances in Wave Digital Filter (WDF) theory allow us to implement circuits with nullors in a systematic fashion, WDFs prove to be useful tools for inverse VA modeling. WDF realizations of a nonlinear audio system and its inverse are presented as an example of application.

Download

Virtual Analog (VA) modeling aims at digitally emulating analog audio equipment while preserving its characteristic nonlinear behavior and musical expressiveness. In the context of guitar effects, overdrive pedals represent a cornerstone of many signal chains, as they strongly contribute to the perceived dynamics, articulation, and timbral identity of the instrument. Among these, the Fulltone OCD overdrive is considered a standard in both studio and live environments, being widely adopted across rock and metal genres. In this article, we present an explicit Wave Digital (WD) model of the Fulltone OCD (v2) pedal. By exploiting the circuit topology, the MOSFETs and the germanium diode composing the asymmetric clipping stage are grouped into a single equivalent nonlinear element, enabling an explicit WD realization that avoids costly iterative solvers. The resulting nonlinear characteristic is approximated by means of a Canonical Piecewise-Linear (CPWL) function, yielding a compact and efficient explicit model suitable for real-time implementation. The proposed model is validated against reference simulations and implemented both in MATLAB and as a real-time audio plug-in using the JUCE framework.

Download

A major problem in the emulation of discrete-time nonlinear systems, such as those encountered in Virtual Analog modeling, is aliasing distortion. A trivial approach to reduce aliasing is oversampling. However, this solution may be too computationally demanding for real-time applications. More advanced techniques to suppress aliased components are arbitrary-order Antiderivative Antialiasing (ADAA) methods that approximate the reference nonlinear function using a combination of its antiderivatives of different orders. While in its original formulation it is applied only to memoryless systems, recently, the applicability of first-order ADAA has been extended to stateful systems employing their statespace description. This paper presents an alternative formulation that successfully applies arbitrary-order ADAA methods to Wave Digital Filter models of dynamic circuits with one nonlinear element. It is shown that the proposed approach allows us to design ADAA models of the nonlinear elements in a fully local and modular fashion, independently of the considered reference circuit. Further peculiar features of the proposed approach, along with two examples of applications, are discussed.

Download