Paper Archive

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.

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Digital oscillators with discontinuities in their time domain signal derivative suffer from an increased noise floor due to the unbound spectrum generated by these discontinuities. Common antialiasing schemes that aim to suppress the unwanted fold-back of higher frequencies can become computationally expensive, as they often involve repeated sample rate manipulation and filtering. In this paper, the authors present an effective approach to applying the four-point polyBLAMP method to the continuous order polygonal oscillator by deriving a closed form expression for the derivative jumps which is only valid at the discontinuities. Compared to the traditional oversampling approach, the resulting SNR improvements of 20 dB correspond to 2–4× oversampling at 25× lower computational complexity, all while offering a higher suppression of aliasing artifacts in the audible range.

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A mechanical system is said to be bistable when its moving parts can rest at two equilibrium positions. The aim of this work is to model the vibration behaviour of a bistable system and use it to create a sound effect, taking advantage of the nonlinearities that characterize such systems. The velocity signal of the bistable system excited by an audio signal is the output of the digital effect. The latter is coded in C++ language and compiled into VST3 format that can be run as an audio plugin within most of the commercial digital audio workstation software in the market and as a standalone application. A Web Audio API demonstration is also available online as a support material.

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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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The band-limited impulse invariance method is a recently proposed approach for the discrete-time modeling of an LTI continuoustime system. Both the magnitude and phase responses are accurately modeled by means of discrete-time filters. It is an extension of the conventional impulse invariance method, which is based on the time-domain sampling of the continuous-time response. The resulting IIR filter typically exhibits spectral aliasing artifacts. In the band-limited impulse invariance method, an FIR filter is combined in parallel with the IIR filter, in such a way that the frequency response of the FIR part reduces the aliasing contributions. This method was shown to improve the frequency-domain accuracy while maintaining the compact temporal structure of the discrete-time model. In this paper, a new version of the bandlimited impulse invariance method is introduced, where the FIR coefficients are derived in closed form by examining the discontinuities that occur in the continuous-time domain. An analytical anti-aliasing filtering is performed by replacing the discontinuities with band-limited transients. The band-limited discontinuities are designed by using the anti-derivatives of the Lagrange interpolation kernel. The proposed method is demonstrated by a wave scattering example, where the acoustical impulse responses on a rigid spherical scatter are simulated.

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This article is concerned with the accurate simulation of passive nonlinear dynamical systems with a particular attention paid on aliasing reduction in the pass-band. The approach is based on the combination of Port-Hamiltonian Systems, continuous-time statespace trajectories reconstruction and exact continuous-time antialiasing filter realization. The proposed framework is applied on a nonlinear LC oscillator circuit to study the effectiveness of the method.

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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.

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This paper is concerned with the conception of methods tailored for the numerical simulation of power-balanced systems that are well-posed but implicitly described. The motivation is threefold: some electronic components (such as the ideal diode) can only be implicitly described, arbitrary connection of components can lead to implicit topological constraints, finally stable discretization schemes also lead to implicit algebraic equations. In this paper we start from the representation of circuits using a power-balanced Kirchhoff-Dirac structure, electronic components are described by a local state that is observed through a pair of power-conjugated algebro-differential operators (V, I) to yield the branch voltages and currents, the arc length is used to parametrize switching and non-Lipschitz components, and a power balanced functional time-discretization is proposed. Finally, the method is illustrated on two simple but non-trivial examples.

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A significant part of the appeal of tape-based delay effects is the manner in which the pitch of their output responds to changes in delay-time. Straightforward approaches to implementation of delays with tape-like modulation behavior result in algorithms with time complexity proportional to the tape speed, leading to noticeable increases of CPU load at smaller delay times. We propose a method which has constant time complexity, except during tape speedup transitions, where the complexity grows logarithmically, or, if proper antialiasing is desired, linearly with respect to the speedup factor.

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Möbius transforms provide for the definition of a family of onestep discretization methods offering a framework for alleviating well-known limitations of common one-step methods, such as the trapezoidal method, at no cost in model compactness or complexity. In this paper, we extend the existing theory around these methods. Here, we show how it can be applied to common frameworks used to structure virtual analog models. Then, we propose practical strategies to tune the transform parameters for best simulation results. Finally, we show how such strategies enable us to formulate much improved non-oversampled virtual analog models for several historical audio circuits.

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