Paper Archive

Neural networks have found application within the Wave Digital Filters (WDFs) framework as data-driven input-output blocks for modeling single one-port or multi-port nonlinear devices in circuit systems. However, traditional neural networks lack predictable bounds for their output derivatives, essential to ensure convergence when simulating circuits with multiple nonlinear elements using fixed-point iterative methods, e.g., the Scattering Iterative Method (SIM). In this study, we address such issue by employing Lipschitz-bounded neural networks for regressing nonlinear WD scattering relations of one-port nonlinearities.

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

The recently developed extension of Wave Digital Filters based on vector wave variables has broadened the class of circuits with linear two-port elements that can be modeled in a modular and explicit fashion in the Wave Digital (WD) domain. In this paper, we apply the vector definition of wave variables to nonlinear twoport elements. In particular, we present two vector WD models of a Bipolar Junction Transistor (BJT) using characteristic equations derived from an extended Ebers-Moll model. One, implicit, is based on a modified Newton-Raphson method; the other, explicit, is based on a neural network trained in the WD domain and it is shown to allow fully explicit implementation of circuits with a single BJT, which can be executed in real time.

Download

Despite the prevalence of modern audio technology, vacuum tube amplifiers continue to play a vital role in the music industry. For this reason, over the years, many different digital techniques have been introduced for accomplishing their emulation. In this paper, we propose a novel quadric surface model for tube simulations able to overcome the Cardarilli model in terms of efficiency whilst retaining comparable accuracy when grid current is negligible. After showing the model capability to well outline tubes starting from measurement data, we perform an efficiency comparison by implementing the considered tube models as nonlinear 3-port elements in the Wave Digital domain. We do this by taking into account the typical common-cathode gain stage employed in vacuum tube guitar amplifiers. The proposed model turns out to be characterized by a speedup of 4.6× with respect to the Cardarilli model, proving thus to be promising for real-time Virtual Analog applications.

Download

Recently, with the advent of new performing headsets and goggles, the demand for Virtual and Augmented Reality applications has experienced a steep increase. In order to coherently navigate the virtual rooms, the acoustics of the scene must be emulated in the most accurate and efficient way possible. Amongst others, Feedback Delay Networks (FDNs) have proved to be valuable tools for tackling such a task. In this article, we expand and adapt a method recently proposed for the data-driven optimization of single-inputsingle-output FDNs to the multiple-input-multiple-output (MIMO) case for addressing spatial/space-time processing applications. By testing our methodology on items taken from two different datasets, we show that the parameters of MIMO FDNs can be jointly optimized to match some perceptual characteristics of given multichannel room impulse responses, overcoming approaches available in the literature, and paving the way toward increasingly efficient and accurate real-time virtual room acoustics rendering.

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

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