Download Automatic Decomposition of Non-linear Equation Systems in Audio Effect Circuit Simulation In the digital simulation of non-linear audio effect circuits, the arising non-linear equation system generally poses the main challenge for a computationally cheap implementation. As the computational complexity grows super-linearly with the number of equations, it is beneficial to decompose the equation system into several smaller systems, if possible. In this paper we therefore develop an approach to determine such a decomposition automatically. We limit ourselves to cases where an exact decomposition is possible, however, and do not consider approximate decompositions.
Download WDF Modeling of a Korg MS-50 Based Non-linear Diode Bridge VCF The voltage-controlled low-pass filter of the Korg MS-50 synthesizer is built around a non-linear diode bridge as the cutoff frequency control element, which greatly contributes to the sound of this vintage synthesizer. In this paper, we introduce the overall filter circuitry and give an in-depth analysis of this diode bridge. It is further shown how to turn the small signal equivalence circuit of the bridge into the necessary two-resistor configuration to uncover the underlying Sallen-Key structure. In a second step, recent advances in the field of WDFs are used to turn a simplified version of the circuit into a virtual-analog model. This model is then examined both in the small-signal linear domain as well as in the non-linear region with inputs of different amplitudes and frequencies to characterize the behavior of such diode bridges as cutoff frequency control elements.
Download Comparison of Germanium Bipolar Junction Transistor Models for Real-time Circuit Simulation The Ebers-Moll model has been widely used to represent Bipolar Junction Transistors (BJTs) in Virtual Analogue (VA) circuits. An investigation into the validity of this model is presented in which the Ebers-Moll model is compared to BJT models of higher complexity, introducing the Gummel-Poon model to the VA field. A comparison is performed using two complementary approaches: on fit to measurements taken directly from BJTs, and on application to physical circuit models. Targeted parameter extraction strategies are proposed for each model. There are two case studies, both famous vintage guitar effects featuring germanium BJTs. Results demonstrate the effects of incorporating additional complexity into the component model, weighing the trade-off between differences in the output and computational cost.
Download Automatic Control of the Dynamic Range Compressor Using a Regression Model and a Reference Sound Practical experience with audio effects as well as knowledge of their parameters and how they change the sound is crucial when controlling digital audio effects. This often presents barriers for musicians and casual users in the application of effects. These users are more accustomed to describing the desired sound verbally or using examples, rather than understanding and configuring low-level signal processing parameters. This paper addresses this issue by providing a novel control method for audio effects. While a significant body of works focus on the use of semantic descriptors and visual interfaces, little attention has been given to an important modality, the use of sound examples to control effects. We use a set of acoustic features to capture important characteristics of sound examples and evaluate different regression models that map these features to effect control parameters. Focusing on dynamic range compression, results show that our approach provides a promising first step in this direction.
Download Fixed-rate Modeling of Audio Lumped Systems: A Comparison Between Trapezoidal and Implicit Midpoint Methods This paper presents a comparison framework to study the relative benefits of the typical trapezoidal method with the lesser-used implicit midpoint method for the simulation of audio lumped systems at a fixed rate. We provide preliminary tools for understanding the behavior and error associated with each method in connection with typical analysis approaches. We also show implementation strategies for those methods, including how an implicit midpoint method solution can be generated from a trapezoidal method solution and vice versa. Finally, we present some empirical analysis of the behavior of each method for a simple diode clipper circuit and provide an approach to help interpret their relative performance and how to pick the more appropriate method depending on desirable properties. The presented tools are also intended as a general approach to interpret the performance of discretization approaches at large in the context of fixed-rate simulation.
Download Generalizing Root Variable Choice in Wave Digital Filters with Grouped Nonlinearities Previous grouped-nonlinearity formulations for Wave Digital Filter (WDF) modeling of nonlinear audio circuits assumed that nonlinear (NL) devices with memoryless voltage–current characteristics were modeled as voltage-controlled current sources (VCCSs). These formulations cannot accommodate nonlinear devices whose equations cannot be written as NL VCCSs, and they cannot accommodate circuits with cutsets composed entirely of current sources (including NL VCCSs). In this paper we generalize independent and dependent variable choice at the root of WDF trees to accommodate both these cases, and review two graph theorems for avoiding forbidden cutsets and loops in general.
Download Block-oriented Gray Box Modeling of Guitar Amplifiers In this work, analog guitar amplifiers are modeled with an automated procedure using iterative optimization techniques. The digital model is divided into functional blocks, consisting of lineartime-invariant (LTI) filters and nonlinear blocks with nonlinear mapping functions and memory. The model is adapted in several steps. First the filters are measured and afterwards the parameters of the digital model are adapted for different input signals to minimize the error between itself and the analog reference system. This is done for a small number of analog reference devices. Afterwards the adapted model is evaluated with objective scores and a listening test is performed to rate the quality of the adapted models.
Download Virtual Analog Buchla 259 Wavefolder An antialiased digital model of the wavefolding circuit inside the Buchla 259 Complex Waveform Generator is presented. Wavefolding is a type of nonlinear waveshaping used to generate complex harmonically-rich sounds from simple periodic waveforms. Unlike other analog wavefolder designs, Buchla’s design features five op-amp-based folding stages arranged in parallel alongside a direct signal path. The nonlinear behavior of the system is accurately modeled in the digital domain using memoryless mappings of the input–output voltage relationships inside the circuit. We pay special attention to suppressing the aliasing introduced by the nonlinear frequency-expanding behavior of the wavefolder. For this, we propose using the bandlimited ramp (BLAMP) method with eight times oversampling. Results obtained are validated against SPICE simulations and a highly oversampled digital model. The proposed virtual analog wavefolder retains the salient features of the original circuit and is applicable to digital sound synthesis.
Download Network Variable Preserving Step-size Control in Wave Digital Filters In this paper a new technique is introduced that allows for the variable step-size simulation of wave digital filters. The technique is based on the preservation of the underlying network variables which prevents fluctuation in the stored energy in reactive network elements when the step-size is changed. This method allows for the step-size variation of wave digital filters discretized with any passive discretization technique and works with both linear and nonlinear reference circuits. The usefulness of the technique with regards to audio circuit simulation is demonstrated via the case study of a relaxation oscillator where it is shown how the variable step-size technique can be used to mitigate frequency error that would otherwise occur with a fixed step-size simulation. Additionally, an example of how aliasing suppression techniques can be combined with physical modeling is given with an example of the polyBLEP antialiasing technique being applied to the output voltage signal of the relaxation oscillator.
Download On the Design and Use of Once-differentiable High Dynamic Resolution Atoms for the Distribution Derivative Method The accuracy of the Distribution Derivative Method (DDM) [1] is evaluated on mixtures of chirp signals. It is shown that accurate estimation can be obtained when the sets of atoms for which the inner product is large are disjoint. This amounts to designing atoms with windows whose Fourier transform exhibits low sidelobes but which are once-differentiable in the time-domain. A technique for designing once-differentiable approximations to windows is presented and the accuracy of these windows in estimating the parameters of sinusoidal chirps in mixture is evaluated.