Download Identification of Nonlinear Circuits as Port-Hamiltonian Systems
This paper addresses identification of nonlinear circuits for power-balanced virtual analog modeling and simulation. The proposed method combines a port-Hamiltonian system formulation with kernel-based methods to retrieve model laws from measurements. This combination allows for the estimated model to retain physical properties that are crucial for the accuracy of simulations, while representing a variety of nonlinear behaviors. As an illustration, the method is used to identify a nonlinear passive peaking EQ.
Download Arbitrary-Order IIR Antiderivative Antialiasing
Nonlinear digital circuits and waveshaping are active areas of study, specifically for what concerns numerical and aliasing issues. In the past, an effective method was proposed to discretize nonlinear static functions with reduced aliasing based on the antiderivative of the nonlinear function. Such a method is based on the continuoustime convolution with an FIR antialiasing filter kernel, such as a rectangular kernel. These kernels, however, are far from optimal for the reduction of aliasing. In this paper we introduce the use of arbitrary IIR rational transfer functions that allow a closer approximation of the ideal antialiasing filter, required in the fictitious continuous-time domain before sampling the nonlinear function output. These allow a higher degree of aliasing reduction and can be flexibly adjusted to balance performance and computational cost.
Download An Equivalent Circuit Interpretation of Antiderivative Antialiasing
The recently proposed antiderivative antialiasing (ADAA) technique for stateful systems involves two key features: 1) replacing a nonlinearity in a physical model or virtual analog simulation with an antialiased nonlinear system involving antiderivatives of the nonlinearity and time delays and 2) introducing a digital filter in cascade with each original delay in the system. Both of these features introduce the same delay, which is compensated by adjusting the sampling period. The result is a simulation with reduced aliasing distortion. In this paper, we study ADAA using equivalent circuits, answering the question: “Which electrical circuit, discretized using the bilinear transform, yields the ADAA system?” This gives us a new way of looking at the stability of ADAA and how introducing extra filtering distorts a system’s response. We focus on the Wave Digital Filter (WDF) version of this technique.
Download Non-Iterative Schemes for the Simulation of Nonlinear Audio Circuits
In this work, a number of numerical schemes are presented in the context of virtual-analog simulation. The schemes are linearlyimplicit in character, and hence directly solvable without iterative methods. Schemes of increasing order of accuracy are constructed, and convergence and stability conditions are proven formally. The schemes are able to handle stiff problems very efficiently, because of their fast update, and can be run at higher sample rates to reduce aliasing. The cases of the diode clipper and ring modulator are investigated in detail, including several numerical examples.
Download Applications of Port Hamiltonian Methods to Non-Iterative Stable Simulations of the Korg35 and Moog 4-Pole Vcf
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.
Download Differentiable White-Box Virtual Analog Modeling
Component-wise circuit modeling, also known as “white-box” modeling, is a well established and much discussed technique in virtual analog modeling. This approach is generally limited in accuracy by lack of access to the exact component values present in a real example of the circuit. In this paper we show how this problem can be addressed by implementing the white-box model in a differentiable form, and allowing approximate component values to be learned from raw input–output audio measured from a real device.
Download Practical Virtual Analog Modeling Using Möbius Transforms
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.
Download Amp-Space: A Large-Scale Dataset for Fine-Grained Timbre Transformation
We release Amp-Space, a large-scale dataset of paired audio samples: a source audio signal, and an output signal, the result of a timbre transformation. The types of transformations we study are from blackbox musical tools (amplifiers, stompboxes, studio effects) traditionally used to shape the sound of guitar, bass, or synthesizer sounds. For each sample of transformed audio, the set of parameters used to create it are given. Samples are from both real and simulated devices, the latter allowing for orders of magnitude greater data than found in comparable datasets. We demonstrate potential use cases of this data by (a) pre-training a conditional WaveNet model on synthetic data and show that it reduces the number of samples necessary to digitally reproduce a real musical device, and (b) training a variational autoencoder to shape a continuous space of timbre transformations for creating new sounds through interpolation.
Download Damped Chirp Mixture Estimation via Nonlinear Bayesian Regression
Estimating mixtures of damped chirp sinusoids in noise is a problem that affects audio analysis, coding, and synthesis applications. Phase-based non-stationary parameter estimators assume that sinusoids can be resolved in the Fourier transform domain, whereas high-resolution methods estimate superimposed components with accuracy close to the theoretical limits, but only for sinusoids with constant frequencies. We present a new method for estimating the parameters of superimposed damped chirps that has an accuracy competitive with existing non-stationary estimators but also has a high-resolution like subspace techniques. After providing the analytical expression for a Gaussian-windowed damped chirp signal’s Fourier transform, we propose an efficient variational EM algorithm for nonlinear Bayesian regression that jointly estimates the amplitudes, phases, frequencies, chirp rates, and decay rates of multiple non-stationary components that may be obfuscated under the same local maximum in the frequency spectrum. Quantitative results show that the new method not only has an estimation accuracy that is close to the Cramér-Rao bound, but also a high resolution that outperforms the state-of-the-art.
Download Sitrano: A Matlab App for Sines-Transients-Noise Decomposition of Audio Signals
Decomposition of sounds into their sinusoidal, transient, and noise components is an active research topic and a widely-used tool in audio processing. Multiple solutions have been proposed in recent years, using time–frequency representations to identify either horizontal and vertical structures or orientations and anisotropy in the spectrogram of the sound. In this paper, we present SiTraNo: an easy-to-use MATLAB application with a graphic user interface for audio decomposition that enables visualization and access to the sinusoidal, transient, and noise classes, individually. This application allows the user to choose between different well-known separation methods to analyze an input sound file, to instantaneously control and remix its spectral components, and to visually check the quality of the separation, before producing the desired output file. The visualization of common artifacts, such as birdies and dropouts, is demonstrated. This application promotes experimenting with the sound decomposition process by observing the effect of variations for each spectral component on the original sound and by comparing different methods against each other, evaluating the separation quality both audibly and visually. SiTraNo and its source code are available on a companion website and repository.