Paper Archive

This paper presents an application of the port Hamiltonian formalism to the nonlinear simulation of the OTA-based Korg35 filter circuit and the Moog 4-pole ladder filter circuit. Lyapunov analysis is used with their state-space representations to guarantee zero-input stability over the range of parameters consistent with the actual circuits. A zero-input stable non-iterative discrete-time scheme based on a discrete gradient and a change of state variables is shown along with numerical simulations. Simulations show behavior consistent with the actual operation of the circuits, e.g., self-oscillation, and are found to be stable and have lower computational cost compared to iterative methods.

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Nonlinear waveshaping is a common technique in musical signal processing, both in a static memoryless context and within feedback systems. Such waveshaping is usually applied directly to a sampled signal, generating harmonics that exceed the Nyquist frequency and cause aliasing distortion. This problem is traditionally tackled by oversampling the system. In this paper, we present a novel method for reducing this aliasing by constructing a continuous-time approximation of the discrete-time signal, applying the nonlinearity to it, and filtering in continuous-time using analytically applied convolution. The presented technique markedly reduces aliasing distortion, especially in combination with low order oversampling. The approach is also extended to allow it to be used within a feedback system.

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This work analyzes analog ring modulators based on bipolar transistors, such as the EMS VCS3 and the Doepfer A-114. It is shown that the perfectly symmetric standard model from literature [1][2] does not suffice to describe crucial first-order effects. A detailed analysis of the circuit using mismatched parts is performed. The insights gained from this analysis are used to formulate a digital model which can be easily implemented and which captures the essential audible effects.

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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.

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In this paper we present an approach to using traditional digital IIR filter structures inside deep-learning networks trained using backpropagation. We establish the link between such structures and recurrent neural networks. Three different differentiable IIR filter topologies are presented and compared against each other and an established baseline. Additionally, a simple Wiener-Hammerstein model using differentiable IIRs as its filtering component is presented and trained on a guitar signal played through a Boss DS-1 guitar pedal.

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This paper explores the digital emulation of analog dynamic range compressors, proposing a grey-box model that uses a combination of traditional signal processing techniques and machine learning. The main idea is to use the structure of a traditional digital compressor in a machine learning framework, so it can be trained end-to-end to create a virtual analog model of a compressor from data. The complexity of the model can be adjusted, allowing a trade-off between the model accuracy and computational cost. The proposed model has interpretable components, so its behaviour can be controlled more readily after training in comparison to a black-box model. The result is a model that achieves similar accuracy to a black-box baseline, whilst requiring less than 10% of the number of operations per sample at runtime.

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Some early analog voltage-controlled amplifiers (VCAs) utilized semiconductor diodes as a variable-gain element. Diode-based VCAs exhibit a unique sound quality, with distortion dependent both on signal level and gain control. In this work, we examine the behavior of a simplified circuit for a diode-based VCA and propose a nonlinear, explicit, stateless digital model. This approach avoids traditional iterative algorithms, which can be computationally intensive. The resulting digital model retains the sonic characteristics of the analog model and is suitable for real-time simulation. We present an analysis of the gain characteristics and harmonic distortion produced by this model, as well as practical guidance for implementation. We apply this approach to a set of alternative analog topologies and introduce a family of digital VCA models based on fixed nonlinearities with variable operating points.

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In this work, we present a data-driven approach to modeling tone stack circuits in guitar amplifiers and distortion pedals. To this aim, the proposed modeling approach uses a feedforward fully connected neural network to predict the parameters of a coupledform state-space filter, ensuring the numerical stability of the resulting time-varying system. The neural network is conditioned on the tone controls of the target tone stack and is optimized jointly with the coupled-form state-space filter to match the target frequency response. To assess the proposed approach, we model three popular tone stack schematics with both matched-order and overparameterized filters and conduct an objective comparison with well-established approaches that use cascaded biquad filters. Results from the conducted experiments demonstrate improved accuracy of the proposed modeling approach, especially in the case of over-parameterized state-space filters while guaranteeing numerical stability. Our method can be deployed, after training, in realtime audio processors.

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In the area of digital musical effect implementation, attention has lately been focused on computer workstations designed for digital processing of sound, which perform all operations with audio signals in real time. They are in fact a combination of powerful computer program and hardware cards with digital signal processors. Thanks to the power enhancement of personal computer core, performing these operations in the CPU is currently possible. However, in most cases, digital signal processors are still used for these purposes because digital musical effect modelling is more effective and more precise with the digital signal processor. In addition to this, processing in digital signal processor saves the CPU computing power for other functions.

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The diode clipper circuit with an embedded low-pass filter lies at the heart of both diode clipping “Distortion” and “Overdrive” or “Tube Screamer” effects pedals. An accurate simulation of this circuit requires the solution of a nonlinear ordinary differential equation (ODE). Numerical methods with stiff stability – Backward Euler, Trapezoidal Rule, and second-order Backward Difference Formula – allow the use of relatively low sampling rates at the cost of accuracy and aliasing. However, these methods require iteration at each time step to solve a nonlinear equation, and the tradeoff for this complexity must be evaluated against simple explicit methods such as Forward Euler and fourth order Runge-Kutta, which require very high sampling rates for stability. This paper surveys and compares the basic ODE solvers as they apply to simulating circuits for audio processing. These methods are compared to a static nonlinearity with a pre-filter. It is found that implicit or semiimplicit solvers are preferred and that the filter/static nonlinearity approximation is often perceptually adequate.

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