Automatic Differentiating Wave Digital Filters with Multiple Nonlinearities

Kolonko, Lech; Velten, Jorg; Kummert, Anton

doi:10.23919/eusipco47968.2020.9287674

Cited by 8 publications

(2 citation statements)

References 10 publications

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“…As an example, in [17] a hybrid iterative scheme, which discusses as particular cases fixedpoint, Newton-Raphson (NR), and Newton-Jacobi methods, is presented, and the flexibility of the WD approach is highlighted. An alternative NR approach is proposed in [18], where the multidimensional WDF formalism [13] is integrated with the concept of automatic differentiation in order to accommodate multiple nonlinearities. However, there were no in-depth studies on the optimal selection of the free parameters in the WD domain (port resistances) until the publication of [19], where a WD fixedpoint method, called Scattering Iterative Method (SIM), was proposed.…”

Section: Introductionmentioning

confidence: 99%

Parallel Wave Digital Filter Implementations of Audio Circuits with Multiple Nonlinearities

Giampiccolo¹,

Natoli²,

Bernardini³

et al. 2022

J. Audio Eng. Soc.

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Modern audio systems and musical effects feature multi-core processing units. The development of parallel audio processing algorithms capable of exploiting the architecture of such hardware is thus in order. In this paper, we present a parallel version of the Hierarchical Scattering Iterative Method (HSIM), a technique based on Wave Digital Filter principles recently proposed for the emulation of multiphysics audio circuits containing multiple nonlinear oneports and nonlinear transformers. HSIM operates in a modular fashion, and it is characterized by a high number of embarrassingly parallelizable operations, making it a good candidate for parallel execution. After analyzing HSIM from the parallel computing perspective, we propose three different strategies for the distribution of HSIM workload among threads of execution, and we show how to compute the maximum achievable speedup. The emulation of a possible output stage of a vacuum-tube guitar amplifier is considered, and a performance comparison between parallel and serial implementations of HSIM is presented, pointing out a speedup of nearly 30%. The proposed method proves thus to be promising for Virtual Analog modeling applications, leading the way towards the parallel digital emulation of increasingly complex audio circuits.

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Section: Introductionmentioning

confidence: 99%

Parallel Wave Digital Filter Implementations of Audio Circuits with Multiple Nonlinearities

Giampiccolo¹,

Natoli²,

Bernardini³

et al. 2022

J. Audio Eng. Soc.

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show abstract

“…Other Newton's approximated schemes using the secant and pseudo-secant method applied to a diode clipper circuit with two diodes were then discussed in [42]. An NR method based on automatic differentiation is applied in [51] for solving the same circuit simulated in [42]. Further NR methods using backtracking and improved initial guesses proved to fit WD models of a diode clipper circuit and a circuit with a 2-port transistor in [43].…”

Section: Introductionmentioning

confidence: 99%

A Wave Digital Newton-Raphson Method for Virtual Analog Modeling of Audio Circuits with Multiple One-Port Nonlinearities

Bernardini

Bozzo

Fontana

et al. 2021

IEEE/ACM Trans. Audio Speech Lang. Process.

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The digital implementation of a nonlinear audio circuit often employs the Newton-Raphson (NR) method for solving the corresponding system of implicit ordinary differential equations in the discrete-time domain. Although its quadratic convergence speed makes NR attractive for real-time audio applications, quadratic convergence is not always guaranteed, since it depends on initial conditions, and also divergence might occur. For this reason, especially in the context of Virtual Analog modeling, techniques for increasing the robustness of NR are in order. Among the various approaches, the Wave Digital (WD) formalism recently showed potential to rethink traditional circuit simulation methods. In this manuscript, we discuss an original formulation of the NR method in the WD domain for the solution of audio circuits with multiple one-port nonlinearities. We provide an in-depth theoretical analysis of the proposed iterative method and we show how its quadratic convergence strongly depends on the free parameters (called port resistances) introduced when modeling the reference circuit in the WD domain. In particular, we demonstrate that the size of the basin where the WD NR solver can be initialized to converge on a solution with quadratic speed is a function of the free parameters. We also show that by setting each port resistance value as close as possible to the derivative w.r.t. current of the nonlinear element v-i characteristic we keep the basin size large. We finally implement an audio ring modulator circuit with four diodes in order to test the proposed iterative method.

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Data-Driven Parameter Estimation of Lumped-Element Models via Automatic Differentiation

Mezza,

Giampiccolo,

Bernardini

2023

IEEE Access

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Lumped-element models (LEMs) provide a compact characterization of numerous real-world physical systems, including electrical, acoustic, and mechanical systems. However, even when the target topology is known, deriving model parameters that approximate a possibly distributed system often requires educated guesses or dedicated optimization routines. This article presents a general framework for the data-driven estimation of lumped parameters using automatic differentiation. Inspired by recent work on physical neural networks, we propose to explicitly embed a differentiable LEM in the forward pass of a learning algorithm and discover its parameters via backpropagation. The same approach could also be applied to blindly parameterize an approximating model that shares no isomorphism with the target system, for which it would be thus challenging to exploit prior knowledge of the underlying physics. We evaluate our framework on various linear and nonlinear systems, including time-and frequency-domain learning objectives, and consider real-and complex-valued differentiation strategies. In all our experiments, we were able to achieve a near-perfect match of the system state measurements and retrieve the true model parameters whenever possible. Besides its practical interest, the present approach provides a fully interpretable inputoutput mapping by exposing the topological structure of the underlying physical model, and it may therefore constitute an explainable ad-hoc alternative to otherwise black-box methods.

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Automatic Differentiating Wave Digital Filters with Multiple Nonlinearities

Cited by 8 publications

References 10 publications

Parallel Wave Digital Filter Implementations of Audio Circuits with Multiple Nonlinearities

Parallel Wave Digital Filter Implementations of Audio Circuits with Multiple Nonlinearities

A Wave Digital Newton-Raphson Method for Virtual Analog Modeling of Audio Circuits with Multiple One-Port Nonlinearities

Data-Driven Parameter Estimation of Lumped-Element Models via Automatic Differentiation

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