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 virtual bass system creates an impression of bass perception in sound systems with weak low-frequency reproduction, which is typical of small loudspeakers. Virtual bass systems extend the bandwidth of the low-frequency audio content using either a nonlinear function or a phase vocoder, and add the processed signal to the reproduced sound. Hybrid systems separate transients and steady-state sounds, which are processed separately. It is still challenging to reach a good sound quality using a virtual bass system. This paper proposes a novel method, which separates the tonal, transient, and noisy parts of the audio signal in a fuzzy way, and then processes only the transients and tones. Those upper harmonics, which can be detected above the cutoff frequency, are boosted using timbre-matched weights, but missing upper harmonics are generated to assist the missing fundamental phenomenon. Listening test results show that the proposed algorithm outperforms selected previous methods in terms of perceived bass sound quality. The proposed method can enhance the bass sound perception of small loudspeakers, such as those used in laptop computers and mobile devices.

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Biquad filters are a common tool for filter design. In this writing, we develop two structures for creating biquad filters with nonlinear elements. We provide conditions for the guaranteed stability of the nonlinear filters, and derive expressions for instantaneous pole analysis. Finally, we examine example filters built with these nonlinear structures, and show how the first nonlinear structure can be used in the context of analog modelling.

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Peak and shelving filters are parametric infinite impulse response filters which are used for amplifying or attenuating a certain frequency band. Shelving filters are parametrized by their cut-off frequency and gain, and peak filters by center frequency, bandwidth and gain. Such filters can be cascaded in order to perform audio processing tasks like equalization, spectral shaping and modelling of complex transfer functions. Such a filter cascade allows independent optimization of the mentioned parameters of each filter. For this purpose, a novel approach is proposed for deriving the necessary local gradients with respect to the control parameters and for applying the instantaneous backpropagation algorithm to deduce the gradient flow through a cascaded structure. Additionally, the performance of such a filter cascade adapted with the proposed method, is exhibited for head-related transfer function modelling, as an example application.

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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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The paper presents a unified, flexible framework for the tasks of audio inpainting, declipping, and dequantization. The concept is further extended to cover analogous degradation models in a transformed domain, e.g. quantization of the signal’s time-frequency coefficients. The task of reconstructing an audio signal from degraded observations in two different domains is formulated as an inverse problem, and several algorithmic solutions are developed. The viability of the presented concept is demonstrated on an example where audio reconstruction from partial and quantized observations of both the time-domain signal and its time-frequency coefficients is carried out.

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Modern commodity GPUs offer high numerical throughput per unit of cost, but often sit idle during audio workstation tasks. Various researches in the field have shown that GPUs excel at tasks such as Finite-Difference Time-Domain simulation and wavefield synthesis. Concrete implementations of several such projects are available for use. Benchmarks and use cases generally concentrate on running one project on a GPU. Running multiple such projects simultaneously is less common, and reduces throughput. In this work we list some concerns when running multiple heterogeneous tasks on the GPU. We apply optimization strategies detailed in developer documentation and commercial CUDA literature, and show results through the lens of real-time audio tasks. We benchmark the cases of (i) a homogeneous effect chain made of previously separate effects, and (ii) a synthesizer with distinct, parallelizable sound generators.

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This paper explores Frequency Modulation (FM) for use in music synthesis. We take an in-depth look at Linear FM, LinearThrough-Zero FM, Phase Modulation (PM) and Exponential FM, and discuss their pros and cons for sound synthesis in a digital system. In the process we derive some useful formulas and discuss their implementation details. In particular we derive analytic expressions for DC correcting Exponential FM, and make it match the modulation depth of Linear FM. Finally, we review practical antialiasing solutions.

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We present a method for accurately synthesizing the acoustic response of a water bottle using modal signal processing. We start with extensive measurements of two water bottles with considerations for how the level of water inside the bottles, the area covered by stickers attached to the exterior of the bottles, and the method of striking the bottles affect their sound. We perform modal analysis of these measurements and implement a real-time modal water bottle synthesizer.

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This paper presents a system for morphing between audio recordings in a continuous parameter space. The proposed approach combines matrix decompositions used for audio source separation with displacement interpolation enabled by 1D optimal transport. By interpolating the spectral components obtained using nonnegative matrix factorization of the source and target signals, the system allows varying the timbre of a sound in real time, while maintaining its temporal structure. Using harmonic / percussive source separation as a pre-processing step, the system affords more detailed control of the interpolation in perceptually meaningful dimensions.

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