Virtual Analog effects refer to the class of digital audio effects that recreate the sound of analog equipment. Vacuum tubes, although old-fashioned, still play a crucial role in defining the distinctive tone of certain audio gear, e.g., guitar amplifiers. Among tubes, variable-µ pentodes stand out for their peculiar nonlinear behavior but are notoriously difficult to simulate using conventional methods. In this article, we extend a method previously proposed for the simulation of circuits containing a single nonlinear two-port element to the case of circuits containing a single variable-µ pentode. We show that by combining Wave Digital Filters based on vector waves and neural networks, we are able to solve said class of circuits in a fully explicit fashion, contrary to what can be done in standard simulators. Our approach is validated through the simulation of the Dogzilla preamplifier stage, offering a promising pathway for the efficient and accurate simulation of circuits containing nonlinear elements characterized by an arbitrary number of ports.

Circuits containing multiple nonlinear elements are typically solved by means of iterative techniques. Recently, Wave Digital Filters (WDFs) have demonstrated good performance for the simulation of circuits containing a high number of nonlinearities. In particular, the vast majority of the approaches available in the literature consider WDFs characterized by reciprocal lossless connection networks. In this article, we provide, instead, a comparison of iterative methods for the solution of WDFs characterized by non-lossless junctions with involutory scattering matrices, e.g., connection networks absorbing nullors. We run different tests at different amplitudes and frequencies, unveiling and giving insights into the trade-off between convergence speed and simulation time.

Time-varying circuits, either due to inherent physical phenomena or due to external user interactions, are ubiquitous, especially in audio processing gear. Examples of such circuits include amplification stages based on a single Bipolar Junction Transistor (BJT) with time-varying controls that adjust, for example, the transistor biasing point. In this manuscript, we extend a previously proposed Wave Digital (WD) methodology for the fully explicit simulation of circuits incorporating a single nonlinear two-port element to accommodate time-varying circuits. To this end, we introduce a novel definition for the explicit BJT WD model, using a nonlinear vector wave scattering equation implemented through a neural network architecture. The proposed approach is validated through the discrete-time simulation of a fuzz guitar pedal with two potentiometers, achieving accuracy levels comparable to standard circuit simulation software.

Wave Digital Filter (WDF) theory has been widely used to design nonlinear digital filters that behave like reference analog circuits, especially in the field of Virtual Analog modeling, i.e., the digital emulation of audio circuits. WDF principles allow us to implement circuits with one nonlinearity in an explicit fashion, by properly setting the free parameters that are introduced in the Wave Digital (WD) domain. Although this property does not extend to the WDF realization of circuits with multiple nonlinearities, which instead requires the use of iterative solvers, a proper setting of the free parameters is beneficial also in these cases, in terms of both robustness and efficiency of the implementation. In particular, recent research shows that a common optimal policy for the setting of free parameters can be adopted when either a WD fixed-point method or a WD Newton-Raphson (NR) method is used to solve the same nonlinear circuit. In this work, we present a class of WD extended fixed-point solvers with order from zero to infinity that generalizes the aforementioned iterative methods; the zero-order case corresponds to the existent WD fixed-point method, while the infinite-order case to WD NR. The proposed solvers do not require to compute inverse Jacobian matrices and are characterized by superlinear speed of convergence. Moreover, we show that the very same policy of free parameter setting can be applied independently of the order, causing, in any case, an increase of robustness and convergence speed.

In the past, the field of drum source separation faced significant challenges due to limited data availability, hindering the adoption of cutting-edge deep learning methods that have found success in other related audio applications. In this letter, we introduce StemGMD, a large- scale audio dataset of isolated single-instrument drum stems. Each audio clip is synthesized from MIDI recordings of expressive drum performances using ten real-sounding acoustic drum kits. Totaling 1224 h, StemGMD is the largest audio dataset of drums to date and the first to comprise isolated audio clips for every instrument in a canonical nine-piece drum kit. We leverage StemGMD to develop LarsNet, a novel deep drum source separation model. Through a bank of dedicated U-Nets, LarsNet can separate five stems from a stereo drum mixture faster than real-time and is shown to considerably outperform state-of-the-art nonnegative spectro-temporal factorization methods.

A method for circuit system inversion has been recently employed to develop digital algorithms for loudspeaker virtualization. In this brief, building on such promising results, we propose an algorithm that flips the paradigm by virtualizing sensors rather than actuators. In particular, we derive direct and inverse nonlinear circuital models of guitar pickup systems by assuming string vertical excitations, and we then present a virtualization algorithm based on circuit inversion. The proposed circuital models are then implemented in the discrete-time domain in a fully explicit fashion (i.e., with no use of iterative solvers) by employing Wave Digital Filter principles. Finally, we validate and test the designed algorithm on the physical output voltage of a guitar pickup system, making it sound as if acquired by two other magnetic pickups characterized by a different nonlinear behavior.

Virtual Bass Enhancement (VBE) refers to a class of digital signal processing algorithms that aim at enhancing the perception of low frequencies in audio applications. Such algorithms typically exploit well-known psychoacoustic effects and are particularly valuable for improving the performance of small-size transducers often found in consumer electronics. Though both time- and frequency-domain techniques have been proposed in the literature, none of them capitalizes on the latest achievements of deep learning as far as music processing is concerned. In this letter, we propose a novel time-domain VBE algorithm that incorporates a deep neural network for music demixing as part of the processing pipeline. This technique is shown to improve the bass perception and reduce inharmonic distortion, i.e., the main issue of existing time-domain VBE algorithms. The results of a perceptual test are then presented, showing that the proposed method is able to outperform state-of-the-art algorithms both in terms of bass enhancement and basic audio quality.

In consumer electronics, the advent of ultra-thin devices has raised interest in Virtual Bass Enhancement (VBE) algorithms for enhancing the acoustic performance of their small-size loudspeakers. In fact, due to physical limitations, large volume velocities cannot be achieved, impairing thus the reproduction of low frequencies. VBE techniques exploit psychoacoustic effects originated by the sound signal processing happening in the inner ear and brain. In this paper, we propose a nonlinear circuital model of a generic time-domain VBE system, and we implement it in the discrete-time domain. As required by most applications of interest, the proposed VBE algorithm is able to operate in real-time. A MUSHRA-like test is then employed to evaluate the bass enhancement performance of the proposed algorithm using different nonlinear devices and parameter configurations.

The nullor is a theoretical two-port element suitable to model several multi-port devices common in audio circuitry, such as ideal operational amplifiers, operational transconductance amplifiers, and transistors operating in linear regime. In this manuscript, we present an approach for the Wave Digital (WD) modeling and implementation of circuits with multiple nullors. In particular, we propose an approach to compute scattering matrices of WD topological junctions absorbing nullors that is less computationally demanding than the techniques available in the literature on WD Filters. We show that the proposed approach turns out to be particularly useful when simulating nonlinear circuits through the Scattering Iterative Method (SIM), a WD fixed-point method recently developed for the solution of circuits with multiple nonlinearities, because it requires a frequent update of the scattering matrices. We also provide a novel convergence analysis of SIM applied to WD structures composed of multiple one-port nonlinear elements and a topological junction absorbing nullors. In order to verify the effectiveness of the proposed methodology, we discuss some WD implementations of analog audio circuits with multiple diodes and opamps, including a precision half-wave rectifier and a wave folder circuit.