Non-Iterative Schemes for the Simulation of Nonlinear Audio Circuits

Ducceschi, Michele; Bilbao, Stefan; Webb, Craig J.

doi:10.23919/dafx51585.2021.9768254

Cited by 6 publications

(12 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Compared to fullyimplicit methods, the proposed schemes have the advantage of efficiency, and of constant operation count per time step. The results presented here expnd considerably on previous work by the same authors [25]. Stability results are available in the case of a VA model described by a single ODE (such as the diode clipper), and partial results are available in the case of a vector nonlinearity.…”

Section: Introductionmentioning

confidence: 70%

“…In this section, a new family of methods is proposed, following from preliminary work presented in [25], which allows good numerical behaviour without the need for iterative techniques. These methods exploit the properties of typical nonlinearities that occur in virtual analog modeling, and are thus less general than the methods described in Section II.…”

Section: A Family Of Non-iterative Schemesmentioning

confidence: 99%

“…The construction of higher-order, one-step schemes of this kind falls within the larger context of modified equation methods, typically employed for the numerical integration of partial differential equations [21], [22]. To the knowledge of the authors, the construction of higher-order schemes for model problem (1), under conditions ( 17), (18) was presented for the first time in a previous publication by the authors [25], and the results therein are extended here. Scheme (20) allows explicit updating, when rewritten as:…”

Section: A Zero-input Casementioning

confidence: 99%

See 2 more Smart Citations

Non-Iterative Simulation Methods for Virtual Analog Modelling

Ducceschi

Bilbao

2022

IEEE/ACM Trans. Audio Speech Lang. Process.

Self Cite

View full text Add to dashboard Cite

The simulation of nonlinear components is central to virtual analog simulation. In audio effects, circuit elements often include devices such as diodes and transistors, mostly operating in the strongly nonlinear regime. Mathematical models are of the form of systems of nonlinear ordinary differential equations (ODEs), and traditional integrators, such as the trapezoid and midpoint methods, can be employed as solvers. These methods are fully implicit, and require the solution of a nonlinear algebraic system at each time step, introducing further complications regarding the existence and uniqueness of the solution, as well as the choice of halting conditions for the iterative root finder. On the other hand, fast explicit methods such as Forward Euler, or explicit Runge-Kutta methods, are prone to unstable behaviour at standard audio sample rates, even at moderate amplitudes. For these reasons, in this work a family of linearlyimplicit schemes is presented. These schemes take the form of a perturbation expansion, making the construction of higherorder schemes possible. Compared with classic implicit designs, the proposed methods have the advantage of efficiency, since the update is computed in a single iteration, through the solution of a linear system of equations. Furthermore, the existence and uniqueness of the update are proven by simple inspection of the update matrix. Compared to classic explicit designs, the proposed schemes display stable behaviour at standard audio sample rates. In the case of a single scalar ODE, sufficient conditions for numerical stability can be derived, imposing constraints on the choice of the sampling rate. Several theoretical results are provided, as well as numerical examples for typical stiff equations used in virtual analog modelling.

show abstract

Section: Introductionmentioning

confidence: 70%

Section: A Family Of Non-iterative Schemesmentioning

confidence: 99%

Section: A Zero-input Casementioning

confidence: 99%

See 1 more Smart Citation

Non-Iterative Simulation Methods for Virtual Analog Modelling

Ducceschi

Bilbao

2022

IEEE/ACM Trans. Audio Speech Lang. Process.

Self Cite

View full text Add to dashboard Cite

show abstract

“…(10.13) This implementation is the one presented in [108], but exhibited spurious oscillations and 'sticking' behaviour. This is due to the possibility of negative forces for positive penetrations due to the discontinuity in the definition for g n at η n = 0.…”

Section: An Explicit Definition For G Nmentioning

confidence: 99%

“…The introduction of an additional state variable, which is what Ducceschi's work is based on, was introduced in [106, 107]. Papers [D]and [E] follow an earlier iteration of the non-iterative collision algorithm from[108,65] which exhibited spurious oscillations that Ducceschi et al resolve in[103]. Paper [H] uses the corrected collision model for the collision between the lips exciting the trombone.…”

mentioning

confidence: 99%

The Emulated Ensemble: Real-Time Simulation of Musical Instruments using Finite-Difference Time-Domain Methods

Willemsen

View full text Add to dashboard Cite

General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research. -You may not further distribute the material or use it for any profit-making activity or commercial gain -You may freely distribute the URL identifying the publication in the public portal -

show abstract