On the Virtualization of Audio Transducers

In audio transduction applications, virtualization can be defined as the task of digitally altering the acoustic behavior of an audio sensor or actuator with the aim of mimicking that of a target transducer. Recently, a digital signal preprocessing method for the virtualization of loudspeakers based on inverse equivalent circuit modeling has been proposed. The method applies Leuciuc’s inversion theorem to obtain the inverse circuital model of the physical actuator, which is then exploited to impose a target behavior through the so called Direct–Inverse–Direct Chain. The inverse model is designed by properly augmenting the direct model with a theoretical two-port circuit element called nullor. Drawing on this promising results, in this manuscript, we aim at describing the virtualization task in a broader sense, including both actuator and sensor virtualizations. We provide ready-to-use schemes and block diagrams which apply to all the possible combinations of input and output variables. We then analyze and formalize different versions of the Direct–Inverse–Direct Chain describing how the method changes when applied to sensors and actuators. Finally, we provide examples of applications considering the virtualization of a capacitive microphone and a nonlinear compression driver

Multidomain modeling of nonlinear electromagnetic circuits using wave digital filters

Accurate models of electromagnetic systems can be derived by coupling electric and magnetic equivalent circuits together. The different nature of such physical domains constitutes a big challenge that puts a continuous strain on software simulators. To face this problem, a simulation approach based on Wave Digital Filters (WDFs) is proposed in this manuscript. The method is employed to solve nonlinear electromagnetic systems containing complex magnetic equivalent circuits while maintaining the modularity of the electric and magnetic subsystems. The nonlinearities can be locally handled, enabling the possibility to choose a dedicated model for each one of them. The proposed algorithm is a hierarchical generalization of the Scattering Iterative Method, which has shown, over the past few years, promising performance for the simulation of large nonlinear circuits. In addition, the method constitutes a further step towards the development of novel general-purpose circuit simulators based on WDF principles. In a comparison with mainstream circuit simulation software, the proposed approach turns out to be considerably faster and thus particularly promising for parametric analyses of electromagnetic systems

Wave Digital Modeling and Implementation of Nonlinear Audio Circuits with Nullors

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

Wave Digital Models of Piezoelectric Transducers for Audio Applications

The number of consumer electronics devices integrating piezoelectric (PE) transducers as flat-panel loudspeakers has recently experienced a steep increase. Being very thin, in fact, piezoelectric transducers well cope with the miniaturization process that characterizes the market. However, at the same time, their reduced dimensions cause the sound pressure level to be poor at low frequency, impairing the overall acoustic response. In this paper, we derive novel efficient discrete-time models of PE transducers in the Wave Digital (WD) domain such that they can be integrated in the future into signal processing algorithms for audio output enhancement. WD Filters are, in fact, making headway among audio digital signal processing techniques based on circuit equivalent models thanks to their efficiency, robustness, and accuracy. Starting from circuital representations of the piezo constitutive equations, we derive both lumped and distributed models. In particular, we show how it is possible to implement the frequency-dependent elements characterizing Mason’s model in the WD domain, contrary to what can be done using mainstream Spice-like simulators. Such WD implementations come in handy for the simulation and fast prototyping of PE systems, paving the way toward the design of model-based digital signal processing algorithms for enhancing the transducer acoustic performance

A Time-Domain Virtual Bass Enhancement Circuital Model for Real-Time Music Applications

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

Virtualization of Guitar Pickups through Circuit Inversion

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

Data-Driven Parameter Estimation of Lumped-Element Models via Automatic Differentiation

Lumped-element models (LEMs) provide a compact characterization of numerous real-world physical systems, including electrical, acoustic, and mechanical systems. However, even when the target topology is known, deriving model parameters that approximate a possibly distributed system often requires educated guesses or dedicated optimization routines. This article presents a general framework for the data-driven estimation of lumped parameters using automatic differentiation. Inspired by recent work on physical neural networks, we propose to explicitly embed a differentiable LEM in the forward pass of a learning algorithm and discover its parameters via backpropagation. The same approach could also be applied to blindly parameterize an approximating model that shares no isomorphism with the target system, for which it would be thus challenging to exploit prior knowledge of the underlying physics. We evaluate our framework on various linear and nonlinear systems, including time- and frequency-domain learning objectives, and consider real- and complex-valued differentiation strategies. In all our experiments, we were able to achieve a near-perfect match of the system state measurements and retrieve the true model parameters whenever possible. Besides its practical interest, the present approach provides a fully interpretable input-output mapping by exposing the topological structure of the underlying physical model, and it may therefore constitute an explainable ad-hoc alternative to otherwise black-box methods

Parallel Wave Digital Filter Implementations of Audio Circuits with Multiple Nonlinearities

Modern audio systems and musical effects feature multicore processing units. Thus, the development of parallel audio processing algorithms capable of exploiting the architecture of such hardware is in order. In this paper, a parallel version of the hierarchical scattering iterative method (HSIM), a technique based on wave digital filter principles recently proposed for the emulation of multiphysics audio circuits containing multiple nonlinear one-ports and nonlinear transformers, is presented. HSIM operates in a modular fashion, and it is characterized by a high number of embarrassingly parallelizable operations, making it a good candidate for parallel execution. After analyzing HSIM from the parallel computing perspective, three different strategies for the distribution of HSIM workload among threads of execution are proposed, showing how to compute the maximum achievable speedup. The emulation of a possible output stage of a vacuum-tube guitar amplifier is considered, and a performance comparison between parallel and serial implementations of HSIM is presented, pointing out a speedup of nearly 30%. The proposed method thus proves to be promising for virtual analog modeling applications, leading the way towards the parallel digital emulation of increasingly complex audio circuits