Paper Archive

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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This paper investigates some fourth-order accurate explicit finite difference schemes for the 2-D wave equation obtained using 13-, 17-, 21-, and 25-point discrete Laplacians. Optimisation is conducted in order to minimise numerical dispersion and computational costs. New schemes are presented that are more computationally efficient than nine-point explicit schemes at maintaining less than one percent wave speed error up to some critical frequency. Simulation results are presented.

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A number of musical instruments (electric basses, tanpuras, sitars...) have a particular timbre due to the contact between a vibrating string and an obstacle. In order to simulate the motion of such a string with the purpose of sound synthesis, various technical issues have to be resolved. First, the contact phenomenon, inherently nonlinear and producing high frequency components, must be described in a numerical manner that ensures stability. Second, as a key ingredient for sound perception, a fine-grained frequencydependent description of losses is necessary. In this study, a new conservative scheme based on a modal representation of the displacement is presented, allowing the simulation of a stiff, damped string vibrating against an obstacle with an arbitrary geometry. In this context, damping parameters together with eigenfrequencies of the system can be adjusted individually, allowing for complete control over loss characteristics. Two cases are then numerically investigated: a point obstacle located in the vicinity of the boundary, mimicking the sound of the tanpura, and then a parabolic obstacle for the sound synthesis of the sitar.

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In this paper, iterative zero-finding techniques are proposed to resolve groups of nonlinearities occurring in Wave Digital Filters. Two variants of Newton’s method are proposed and their suitability towards solving the grouped nonlinearities is analyzed. The feasibility of the approach with implications for WDFs containing multiple nonlinearities is demonstrated via case studies investigating the mathematical properties and numerical performance of reference circuits containing diodes and transistors; asymmetric and symmetric diode clippers and a common emitter amplifier.

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Raster scanning is a technique for generating or recording a video image by means of a line-by-line sweep, tantamount to a data mapping scheme between one and two dimensional spaces. While this geometric structure has been widely used on many data transmission and storage systems as well as most video displaying and capturing devices, its application to audio related research or art is rare. In this paper, a data mapping mechanism of raster scanning is proposed as a framework for both image sonification and sound visualization. This mechanism is simple, and produces compelling results when used for sonifying image texture and visualizing sound timbre. In addition to its potential as a cross modal representation, its complementary and analogous property can be applied sequentially to create a chain of sonifications and visualizations using digital filters, thus suggesting a useful creative method of audio processing. Special attention is paid to the rastrogram - raster visualization of sound - as an intuitive visual interface to audio data. In addition to being an efficient means of sound representation that provides meaningful display of significant auditory features, the rastrogram is applied to the area of sound analysis by visualizing characteristics of loop filters used for a Karplus-Strong model. A new sound synthesis method based on texture analysis/synthesis of the rastrogram is also suggested.

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In this short paper, we address the numerical simulation of the single reed excitation mechanism. In particular, we discuss a formalism for approaching the lumped nonlinearity inherent in such a model using a circuit model and the application of wave digital filters (WDFs), which are of interest in that they allow simple stability verification, a property which is not generally guaranteed if one employs straightforward numerical methods. We present first a standard reed model, then its circuit representation, then finally the associated wave digital network. We then enter into some implementation issues, such as the solution of nonlinear algebraic equations, and the removal of delay-free loops, and present simulation results.

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Nonnegative Matrix Factorization is a popular tool for the analysis of audio spectrograms. It is usually initialized with random data, after which it iteratively converges to a local optimum. In this paper we show that N-FINDR and NNLS, popular techniques for dictionary and activation matrix learning in remote sensing, prove useful to create a better starting point for NMF. This reduces the number of iterations necessary to come to a decomposition of similar quality. Adapting algorithms from the hyperspectral image unmixing and remote sensing communities, provides an interesting direction for future research in audio spectrogram factorization.

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In recent years multisampled drum workstations have become increasingly popular. They offer an alternative to recording a full drum kit if a producer, engineer or amateur lacks the equipment, money, space or knowledge to produce a quality recording. These drum workstations strive for realism, often recording up to a hundred different velocity hits of the same drum, including recordings from all microphones for each drum hit and including bleed between these microphones. This paper describes research undertaken to investigate if it is possible to simulate the snare and kick drum bleed into the tom-tom microphones and the subsequent resonance of the tom-tom that is caused, with the aim of reducing the amount of audio data that needs to be stored. A listening test was performed asking participants to identify the real recording from a simulation. The results were not statistically significant to reject the hypothesis that subjects were unable to distinguish the difference between the real and simulated recordings. This suggests listeners were unable to identify the real recording in the majority of cases.

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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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Extraction of stationary and transient components from audio has many potential applications to audio effects for audio content production. In this paper we explore stationary/transient separation using convolutional autoencoders. We propose two novel unsupervised algorithms for individual and and joint separation. We describe our implementation and show examples. Our results show promise for the use of convolutional autoencoders in the extraction of sparse components from audio spectrograms, particularly using monophonic sounds.

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