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.

The ondes Martenot is a classic electronic musical instrument based on heterodyning processing. This article proposes a power-balanced simulation of its circuit, in order to synthesize the sound it produces. To this end, the proposed approach consists in formulating the circuit as a Port-Hamiltonian System, for which power-balanced numerical methods are available. Observations on numerical experiments based upon this formulation allow simplifications of the circuit in order to achieve real-time computation in home-studio conditions.

The attenuation of standard analog low-pass filters corresponds to a multiple value of -6 decibels per octave. This quantified value is related to the order of the filter. The issue addressed here is concerned with the extension of integer orders to non integer orders, such that the attenuation of a low-pass filter can be continuously adjusted. Fractional differential systems are known to provide such asymptotic behaviors and many results about their simulation are available. But even for a fixed cutoff frequency, their combination does not generate an additive group with respect to the order and they involve stability problems. In this paper, a class of low-pass filters with orders between 0 (the filter is a unit gain) and 1 (standard one-pole filter) is defined to restore these properties. These infinite dimensional filters are not fractional differential but admit some well-posed representations into weighted integrals of standard one-pole filters. Based on this, finite dimensional approximations are proposed and recast into the framework of statespace representations-space representations. A special care is given to reduce the computational complexity, through the dimension of the state. In practice, this objective is reached for the complete family, without damaging the perceptive quality, with dimension 13. Then, an accurate low-cost digital version of this family is built in the time-domain. The accuracy of the digital filters is verified on the complete range of parameters (cutoff frequencies and fractional orders). Moreover, the stability is guaranteed, even for time-varying parameters. As an application, a plugin has been implemented which provides a new audio tool for tuning the cutoff frequency and the asymptotic slope in a continuous way. As a very special application, choosing a one-half order combined with a low cutoff frequency (20 Hz or less), the filter fed with a white noise provides a pink noise generator.

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Volterra series are known to be efficient to represent weakly nonlinear systems and the first distortions. Their truncated versions allow one to derive realizations (in the sense of system theory) leading to networks composed of linear filters, sums, and instantaneous products of signals, without instantaneous feedback loops. Nevertheless, if saturation phenomena arise, truncating the series at low order is not sufficient and the convergence can also be lost. In this paper, the case of the Moog ladder filter is investigated. Low-cost simulations based on realizations of Volterra series are given. Their limitations with respect to the amplitude of input signals are exhibited. Methods to increase the validity range and to improve the efficiency of Volterra series expansions are detailed on a single stage of the filter. In particular, changes of states based on the difference between the original state and predictors (parameterized by a tunable delayT) yield satisfying results. The digital simulation of this system preserves the properties mentioned above. It includes two delay lines (where the delayTcan be chosen to be one sample) and nonlinear static functions given by the method.

This paper deals with digital waveguide modeling of wind instruments. It presents the application of state-space representations for the refined acoustic model ofWebster-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). The purpose of this work is to build low-cost digital simulations in the time domain based on theWebster-Lokshinmodel. First, decomposing a resonator into independent elementary parts and isolating delay operators lead to aKelly-Lochbaumnetwork of input/output systems and delays. 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 the time domain. The method is applied to a real trombone, and results of simulations are presented and compared with measurements. This method seems to be a promising approach in term of modularity, complexity of calculation, and accuracy, for any acoustic resonators based on tubes.