Paper Archive

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.

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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.

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Sustained contact interactions like scraping and rolling produce a wide variety of sounds. Previous studies have explored ways to synthesize these sounds efficiently and intuitively but could not fully mimic the rich structure of real instances of these sounds. We present a novel source-filter model for realistic synthesis of scraping and rolling sounds with physically and perceptually relevant controllable parameters constrained by principles of mechanics. Key features of our model include non-linearities to constrain the contact force, naturalistic normal force variation for different motions, and a method for morphing impulse responses within a material to achieve location-dependence. Perceptual experiments show that the presented model is able to synthesize realistic scraping and rolling sounds while conveying physical information similar to that in recorded sounds.

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We propose a new analog filter discretization method that is useful for discretizing systems with features near or above the Nyquist limit. A conformal mapping approach is taken, and we introduce the peaking conformal map and shelving conformal map. The proposed method provides a close match to the original analog frequency response below half the sampling rate and is parameterizable, order preserving, and agnostic to the original filter’s order or type. The proposed method should have applications to discretizing filters that have time-varying parameters or need to be implemented across many different sampling rates.

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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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Piano transcription is a classic problem in music information retrieval. More and more transcription methods based on deep learning have been proposed in recent years. In 2019, Google Brain published a larger piano transcription dataset, MAESTRO. On this dataset, Onsets and Frames transcription approach proposed by Hawthorne achieved a stunning onset F1 score of 94.73%. Unlike the annotation method of Onsets and Frames, Transition-aware model presented in this paper annotates the attack process of piano signals called atack transition in multiple frames, instead of only marking the onset frame. In this way, the piano signals around onset time are taken into account, enabling the detection of piano onset more stable and robust. Transition-aware achieves a higher transcription F1 score than Onsets and Frames on MAESTRO dataset and MAPS dataset, reducing many extra note detection errors. This indicates that Transition-aware approach has better generalization ability on different datasets.

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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.

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Sinusoids are widely used to represent the oscillatory modes of music and speech. The estimation of the sinusoidal parameters directly affects the quality of the representation. A parabolic interpolation of the peaks of the log-magnitude spectrum is commonly used to get a more accurate estimation of the frequencies and the amplitudes of the sinusoids at a relatively low computational cost. Recently, Werner and Germain proposed an improved sinusoidal estimator that performs parabolic interpolation of the peaks of a power-scaled magnitude spectrum. For each analysis window type and size, a power-scaling factor p is pre-calculated via a computationally demanding heuristic. Consequently, the powerscaling estimation method is currently constrained to a few tabulated power-scaling factors for pre-selected window sizes, limiting its practical applications. In this article, we propose a method to obtain the power-scaling factor p for any window size from the tabulated values. Additionally, we investigate the impact of zeropadding on the estimation accuracy of the power-scaled sinusoidal parameter estimator.

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Deep neural networks have been recently applied to the task of automatic synthesizer programming, i.e., finding optimal values of sound synthesis parameters in order to reproduce a given input sound. This paper focuses on generative models, which can infer parameters as well as generate new sets of parameters or perform smooth morphing effects between sounds. We introduce new models to ensure scalability and to increase performance by using heterogeneous representations of parameters as numerical and categorical random variables. Moreover, a spectral variational autoencoder architecture with multi-channel input is proposed in order to improve inference of parameters related to the pitch and intensity of input sounds. Model performance was evaluated according to several criteria such as parameters estimation error and audio reconstruction accuracy. Training and evaluation were performed using a 30k presets dataset which is published with this paper. They demonstrate significant improvements in terms of parameter inference and audio accuracy and show that presented models can be used with subsets or full sets of synthesizer parameters.

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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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