Dynamic adaptation of instantaneous nonlinear bipoles in wave digital networks

IEEE/ACM Trans. Audio Speech Lang. Process.

Maffezzoni

Sarti

2019

Self Cite

There is a growing interest in Virtual Analog modeling algorithms for musical audio processing designed in the Wave Digital (WD) domain. Such algorithms typically employ a discretization strategy based on the trapezoidal rule with fixed sampling step, though this is not the only option. In fact, alternative discretization strategies (possibly with an adaptive sampling step) can be quite advantageous, particularly when dealing with nonlinear systems characterized by stiff equations. In this article, we propose a unified approach for modeling capacitors and inductors in the WD domain using generic linear multi-step discretization methods with variable time-step size, and provide generalized adaptation conditions. We also show that the proposed approach for implementing dynamic (energystoring) elements in the WD domain is particularly suitable to be combined with a recently developed technique for efficiently solving a class of circuits with multiple one-port nonlinearities, called Scattering Iterative Method. Finally, as examples of application, we develop WD models for a Van Der Pol oscillator and a dynamic diode-based ring modulator, which use different discretization methods.

Section: A Capacitorsmentioning

confidence: 99%

“…are the same real coefficients appearing in eq. (22) and the variable step-size h[k] is defined as in eq. (23).…”

Section: B Inductorsmentioning

confidence: 99%

Linear Multistep Discretization Methods With Variable Step-Size in Nonlinear Wave Digital Structures for Virtual Analog Modeling

IEEE/ACM Trans. Audio Speech Lang. Process.

Maffezzoni

Sarti

2019

Self Cite

“…Part IV, containing Chaps. 10, 11 and 12, is mainly devoted to the WD implementation of circuits with multiple nonlinearities using a further method called Scattering Iterative Method (SIM) that has been recently developed starting from the preliminary results presented in [6]. SIM is a relaxation method characterized by an iterative procedure that alternates a local scattering stage, devoted to the computation of waves reflected from each element, and a global scattering stage, devoted to the computation of waves reflected from a WD junction to which all elements are connected.…”

Section: Part Iv: Implementation Of Circuits With Multiple Nonlinearimentioning

confidence: 99%

Advances in Wave Digital Modeling of Linear and Nonlinear Systems: A Summary

Special Topics in Information Technology

2019

Self Cite

This brief summarizes some of the main research results that I obtained during the three years, ranging from November 2015 to October 2018, as a Ph.D. student at Politecnico di Milano under the supervision of Professor Augusto Sarti, and that are contained in my doctoral dissertation, entitled "Advances in Wave Digital Modeling of Linear and Nonlinear Systems". The thesis provides contributions to all the main aspects of Wave Digital (WD) modeling of lumped systems: it introduces generalized definitions of wave variables; it presents novel WD models of one-and multi-port linear and nonlinear circuit elements; it discusses systematic techniques for the WD implementation of arbitrary connection networks and it describes a novel iterative method for the implementation of circuits with multiple nonlinear elements. Though WD methods usually focus on the discrete-time implementation of analog audio circuits; the methodologies addressed in the thesis are general enough as to be applicable to whatever system that can be described by an equivalent electric circuit.

“…It may also happen that δi k = 0; in this case, R > −∞ if δv k ≥ 0 and R = ∅ if δv k < 0, where ∅ denotes the empty set. Let us express the system of inequalities (10) in an alternative form, defining a vectorr…”

Section: Conditions On the Port Resistancementioning

confidence: 99%

“…Most WD structures with one nonlinear (NL) element [5], [6] can be efficiently implemented in a systematic fashion [7]. NL WD elements are generally implemented using look-up tables [8] or iterative solvers [9], even though alternative techniques exist [10]. However, disposing of canonical PieceWise Linear (PWL) representations [11] of nonlinearities in the WD domain would be very useful for many reasons.…”

Section: Introductionmentioning

confidence: 99%

Canonical piecewise-linear representation of curves in the wave digital domain

2017 25th European Signal Processing Conference (EUSIPCO)

Sarti

2017

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Abstract-Global, explicit representations of nonlinearities are desirable when implementing nonlinear Wave Digital (WD) structures, as they free us from the burden of managing lookup tables, performing data interpolation and/or using iterative solvers. In this paper we present a method that, starting from certain parameterized PieceWise-Linear (PWL) curves in the Kirchhoff domain, allows us to express them in the WD domain using a global and explicit representation. We will show how some curves (multi-valued functions in the Kirchhoff domain) can be represented as functions in canonical PWL form in the WD domain. In particular, we will present a procedure, which, in the most general case, also returns the conditions on the reference port resistance under which it is possible to find explicit mappings in the WD domain.