Paper Archive

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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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.

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In recent years, a range of topological methods have emerged for processing digital signals. In this paper we show how the construction of topological filters via sheaves can be used to topologize existing sound synthesis methods. I illustrate this process on two classes of synthesis approaches: (1) based on linear-time invariant digital filters and (2) based on oscillators defined on a circle. We use the computationally-friendly approach to modeling topologies via a simplicial complex, and we attach our classical synthesis methods to them via sheaves. In particular, we explore examples of simplicial topologies that mimic sampled lines and loops. Over these spaces we realize concrete examples of simple discrete harmonic oscillators (resonant filters), and simple comb filter based algorithms (such as Karplus-Strong) as well as frequency modulation.

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The distributed nature of coupling in helical springs presents specific challenges in obtaining efficient computational structures for accurate spring reverb simulation. For direct simulation approaches, such as finite-difference methods, this is typically manifested in significant numerical dispersion within the hearing range. Building on a recent study of a simpler spring model, this paper presents an alternative discretisation approach that employs higher-order spatial approximations and applies centred stencils at the boundaries to address the underlying linear-system eigenvalue problem. Temporal discretisation is then applied to the resultant uncoupled mode system, rendering an efficient and flexible modal reverb structure. Through dispersion analysis it is shown that numerical dispersion errors can be kept extremely small across the hearing range for a relatively low number of system nodes. Analysis of an impulse response simulated using model parameters calculated from a measured spring geometry confirms that the model captures an enhanced set of spring characteristics.

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Fractional order filters have been studied since a long time, along with their applications to many areas of physics and engineering. In particular, several solutions have been proposed in order to approximate their frequency response with that of an ordinary filter. In this paper, we tackle this problem with a new approach: we solve analytically a simplified version of the problem and we find the optimal placement of poles and zeros, giving a mathematical proof and an error estimate. This solution shows improved performance compared to the current state of the art and is suitable for real-time parametric control.

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A method is proposed to encode the acoustic scattering of objects for virtual acoustic applications through a multiple-input and multiple-output framework. The scattering is encoded as a matrix in the spherical harmonic domain, and can be re-used and manipulated (rotated, scaled and translated) to synthesize various sound scenes. The proposed method is applied and validated using Boundary Element Method simulations which shows accurate results between references and synthesis. The method is compatible with existing frameworks such as Ambisonics and image source methods.

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Contemporary musicians commonly face the challenge of finding new, characteristic sounds that can make their compositions more distinct. They often resort to computers and algorithms, which can significantly aid in creative processes by generating unexpected material in controlled probabilistic processes. In particular, algorithms that present emergent behaviors, like genetic algorithms and cellular automata, have fostered a broad diversity of musical explorations. This article proposes an original technique for the computer-assisted creation and manipulation of sound textures. The technique uses Probabilistic Cellular Automata, which are yet seldom explored in the music domain, to blend two audio tracks into a third, different one. The proposed blending process works by dividing the source tracks into frequency bands and then associating each of the automaton’s cell to a frequency band. Only one source, chosen by the cell’s state, is active within each band. The resulting track has a non-repeating textural pattern that follows the changes in the Cellular Automata. This blending process allows the musician to choose the original material and the blend granularity, significantly changing the resulting blends. We demonstrate how to use the proposed blending process in sound design and its application in experimental and popular music.

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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.

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It is difficult to adjust the parameters of a complex synthesizer to create the desired sound. As such, sound matching, the estimation of synthesis parameters that can replicate a certain sound, is a task that has often been researched, utilizing optimization methods such as genetic algorithm (GA). In this paper, we introduce a novelty-based objective for GA-based sound matching. Our contribution is two-fold. First, we show that the novelty objective is able to improve the quality of sound matching by maintaining phenotypic diversity in the population. Second, we introduce a quality diversity approach to the problem of sound matching, aiming to find a diverse set of matching sounds. We show that the novelty objective is effective in producing high-performing solutions that are diverse in terms of specified audio features. This approach allows for a new way of discovering sounds and exploring the capabilities of a synthesizer.

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Virtual analog (VA) modeling using neural networks (NNs) has great potential for rapidly producing high-fidelity models. Recurrent neural networks (RNNs) are especially appealing for VA due to their connection with discrete nodal analysis. Furthermore, VA models based on NNs can be trained efficiently by directly exposing them to the circuit states in a gray-box fashion. However, exposure to ground truth information during training can leave the models susceptible to error accumulation in a free-running mode, also known as “exposure bias” in machine learning literature. This paper presents a unified framework for treating the previously proposed state trajectory network (STN) and gated recurrent unit (GRU) networks as special cases of discrete nodal analysis. We propose a novel circuit state-matching mechanism for the GRU and experimentally compare the previously mentioned networks for their performance in state matching, during training, and in exposure bias, during inference. Experimental results from modeling a diode clipper show that all the tested models exhibit some exposure bias, which can be mitigated by truncated backpropagation through time. Furthermore, the proposed state matching mechanism improves the GRU modeling performance of an overdrive pedal and a phaser pedal, especially in the presence of external modulation, apparent in a phaser circuit.

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