Oral Session 5: Virtual Analog

14:00-15:20 on Wednesday, 4th September

P350 Lecture Theatre, Parkside

Chiar: Julian Parker
Antiderivative Antialiasing for Stateful Systems
Martin Holters

Nonlinear systems, like e.g. guitar distortion effects, play an important role in musical signal processing. One major problem encountered in digital nonlinear systems is aliasing distortion. Consequently, various aliasing reduction methods have been proposed in the literature. One of these is based on using the antiderivative of the nonlinearity and has proven effective, but is limited to memoryless systems. In this work, it is extended to a class of stateful systems which includes but is not limited to systems with a single one-port nonlinearity. Two examples from the realm of virtual analog modeling show its applicability to and effectiveness for commonly encountered guitar distortion effect circuits.

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Fast Approximation of the Lambert W Function for Virtual Analog Modelling
Stefano D'Angelo, Leonardo Gabrielli and Luca Turchet

When modelling circuits one has often to deal with equations containing both a linear and an exponential part. If only a single exponential term is present or predominant, exact or approximate closed-form solutions can be found in terms of the Lambert W function. In this paper, we propose reformulating such expressions in terms of the Wright Omega function when specific conditions are met that are customary in practical cases of interest. This eliminates the need to compute an exponential term at audio rate. Moreover, we propose simple and real-time suitable approximations of the Omega function. We apply our approach to a static and a dynamic nonlinear system, obtaining digital models that have high accuracy, low computational cost, and are stable in all conditions, making the proposed method suitable for virtual analog modelling of circuits containing semiconductor devices.

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A Minimal Passive Model of the Operational Amplifier: Application to Sallen-Key Analog Filters
Rémy Müller and Thomas Helie

This papers stems from the fact that, whereas there are passive models of transistors and tubes, a minimal passive model of the operational amplifier does not seem to exist. A new behavioural model is presented that is memoryless, fully described by its interaction ports, with a minimal number of equations, for which a passive power balance can be defined. The proposed model handles saturation, asymmetric power supply, and can be used with nonideal voltage references. To illustrate the model in audio applications, the non-inverting voltage amplifier and a saturating Sallen-Key lowpass filter are considered.

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Towards Inverse Virtual Analog Modeling
Alberto Bernardini and Augusto Sarti

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.

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