Download Towards Inverse Virtual Analog Modeling 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 Antiderivative Antialiasing in Nonlinear Wave Digital Filters 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 A Quadric Surface Model of Vacuum Tubes for Virtual Analog Applications 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 Explicit Vector Wave Digital Filter Modeling of Circuits with a Single Bipolar Junction Transistor 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 Wave Digital Model of the MXR Phase 90 Based on a Time-Varying Resistor Approximation of JFET Elements 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 Wave Digital Modeling of Circuits with Multiple One-Port Nonlinearities Based on Lipschitz-Bounded Neural Networks 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 Modeling the Frequency-Dependent Sound Energy Decay of Acoustic Environments with Differentiable Feedback Delay Networks Differentiable machine learning techniques have recently proved effective for finding the parameters of Feedback Delay Networks (FDNs) so that their output matches desired perceptual qualities of target room impulse responses. However, we show that existing methods tend to fail at modeling the frequency-dependent behavior of sound energy decay that characterizes real-world environments unless properly trained. In this paper, we introduce a novel perceptual loss function based on the mel-scale energy decay relief, which generalizes the well-known time-domain energy decay curve to multiple frequency bands. We also augment the prototype FDN by incorporating differentiable wideband attenuation and output filters, and train them via backpropagation along with the other model parameters. The proposed approach improves upon existing strategies for designing and training differentiable FDNs, making it more suitable for audio processing applications where realistic and controllable artificial reverberation is desirable, such as gaming, music production, and virtual reality.
Download Differentiable MIMO Feedback Delay Networks for Multichannel Room Impulse Response Modeling 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.