Paper Archive

This paper proposes a new macroscopic physical model of ferromagnetic coils used in audio circuits. To account for realistic saturation and hysteretic phenomena, this model combines statistical physics results, measurement-driven refinements and portHamiltonian formulations that guarantee passivity, thermodynamic consistency and composability according to both electric and thermal ports. As an illustration, the model is used to simulate a passive high-pass filter. Different types of audio inputs are considered and simulations are compared to measurements.

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This paper deals with the time-domain simulation of a simplified electro-mechanical piano. The physical model is composed of a hammer (nonlinear component), a cantilever beam (damped linear resonator) and a pickup (nonlinear transducer). In order to ensure stable simulations, a method is proposed, which preserves passivity, namely, the conservative and dissipative properties of the physical system. This issue is addressed in 3 steps. First, each physical component is described by a passive input-output system, which is recast in the port-Hamiltonian framework. In particular, a passive finite dimensional model of the Euler-Bernoulli beam is derived, based on a standard modal decomposition. Second, these components are connected, providing a nonlinear finite dimensional port-Hamiltonian system. Third, a numerical method is proposed, which preserves the power balance and passivity. Numerical results are presented and analyzed.

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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.

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This work takes place in the context of the development of an active control of instruments with geometrical nonlinearities. The study focuses on Chinese opera gongs that display a characteristic pitch glide in normal playing conditions. In the case of the xiaoluo gong, the fundamental mode of the instrument presents a softening behaviour (frequency glides upward when the amplitude decreases). Controlling the pitch glide requires a nonlinear model of the structure, which can be partially identified with experimental techniques that rely on the formalism of nonlinear normal modes. The fundamental nonlinear mode has been previously experimentally identified as a softening Duffing oscillator. This paper aims at performing a simulation of the control of the oscillator’s pitch glide. For this purpose, the study focuses on a single-degree-offreedom nonlinear mode described by a softening Duffing equation. This Duffing oscillator energy proves to be ill-posed - in particular, the energy becomes negative for large amplitudes of vibration, which is physically inconsistent. Then, the first step of the present study consists in redefining a new energetically well-posed model. In a second part, guaranteed-passive simulations using port-Hamiltonian formalism confirm that the new system is physically and energetically correct compared to the Duffing model. Third, the model is used for control issues in order to modify the softening or hardening behaviour of the fundamental pitch glide. Results are presented and prove the method to be relevant. Perspectives for experimental applications are finally exposed in the last section of the paper.

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Vactrols, which consist of a photoresistor and a light-emitting element that are optically coupled, are key components in optical dynamic compressors. Indeed, the photoresistor’s program-dependent dynamic characteristics make it advantageous for automatic gain control in audio applications. Vactrols are becoming more and more difficult to find, while the interest for optical compression in the audio community does not diminish. They are thus good candidates for virtual analog modeling. In this paper, a model of vactrols that is entirely physical, passive, with a program-dependent dynamic behavior, is proposed. The model is based on first principles that govern semi-conductors, as well as the port-Hamiltonian systems formalism, which allows the modeling of nonlinear, multiphysical behaviors. The proposed model is identified with a real vactrol, then connected to other components in order to simulate a simple optical compressor.

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This article addresses the Doppler effect of a planar vibrating piston in a duct, as a plane wave radiation approximation generated by a loudspeaker membrane. This physical model corresponds to a nonlinear problem, because the linear propagation is excited by a moving boundary condition at the piston face: this introduces a varying propagation time between the piston and a fixed receiver. The existence of a regular function that solves the problem (a socalled “strong” solution) is proven, under a well-posed condition that guarantees that no shock occurs. This function satisfies an implicit equation to be solved. An algorithm based on the perturbation method is proposed, from which an exact solution can be built using power series. The convergence of the power series is numerically checked on several examples. Simulations derived from a truncated power series provide sound examples with audible intermodulation and distortion effects for realistic loudspeaker excursion and speed ranges.

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This work deals with the physical modelling of acoustic pipes for real-time simulation, using the “Digital Waveguide Network” approach and the horn equation. With this approach, a piece of pipe is represented by a two-port system with a loop which involves two delays for wave propagation, and some subsystems without internal delay. A well-known form of this system is the “Kelly-Lochbaum” framework, which allows the reduction of the computation complexity. We focus this work on the simulation of pipes with a convex profile. But, using the “Kelly-Lochbaum” framework with the horn equation, two problems occur: first, even if the outputs are bound, some substates have their values which diverge; second, there is an infinite number of such substates. The system is then unstable and cannot be simulated as such. The solution of this problem is obtained with two steps. First, we show that there is a simple standard form compatible with the “Waveguide” approach, for which there is an infinite number of solutions which preserve the input/output relations. Second, we look for one solution which guarantees the stability of the system and which makes easier the approximation in order to get a low-cost simulation.

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Efficient stable integration methods for nonlinear systems are of great importance for physical modeling sound synthesis. Specifically, a number of musical systems of interest, including vibrating strings, bars or plates may be written as port-Hamiltonian systems with quadratic kinetic energy and non-quadratic potential energy. Efficient schemes have been developed for such systems through the introduction of a scalar auxiliary variable. As a result, the stable real-time simulations of nonlinear musical systems of up to a few thousands of degrees of freedom is possible, even for nearly lossless systems. However, convergence rates can be slow and seem to be system-dependent. Specifically, at audio rates, they may suffer from numerical drift of the auxiliary variable, resulting in dramatic unwanted effects on audio output, such as pitch drifts after several impacts on the same resonator. In this paper, a novel method for mitigating this unwanted drift while preserving power balance is presented, based on a control approach. A set of modified equations is proposed to control the drift artefact by rerouting energy through the scalar auxiliary variable and potential energy state. Numerical experiments are run in order to check convergence on simulations in the case of a cubic nonlinear string. A real-time implementation is provided as a Max/MSP external. 60-note polyphony is achieved on a laptop, and some simple high level control parameters are provided, making the proposed implementation suitable for use in artistic contexts. All code is available in a public repository, along with compiled Max/MSP externals1.

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This article is concerned with the accurate simulation of passive nonlinear dynamical systems with a particular attention paid on aliasing reduction in the pass-band. The approach is based on the combination of Port-Hamiltonian Systems, continuous-time statespace trajectories reconstruction and exact continuous-time antialiasing filter realization. The proposed framework is applied on a nonlinear LC oscillator circuit to study the effectiveness of the method.

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This paper deals with digital waveguide modeling of wind instruments. It presents the application of state-space representations to the acoustic model of Webster-Lokshin. This acoustic model describes the propagation of longitudinal waves in axisymmetric acoustic pipes with a varying cross-section, visco-thermal losses at the walls, and without assuming planar or spherical waves. Moreover, three types of discontinuities of the shape can be taken into account (radius, slope and curvature), which can lead to a good fit of the original shape of pipe. The purpose of this work is to build low-cost digital simulations in the time domain, based on the Webster-Lokshin model. First, decomposing a resonator into independent elementary parts and isolating delay operators lead to a network of input/output systems and delays, of KellyLochbaum network type. Second, for a systematic assembling of elements, their state-space representations are derived in discrete time. Then, standard tools of automatic control are used to reduce the complexity of digital simulations in time domain. In order to validate the method, simulations are presented and compared with measurements.

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