Download Arbitrary-Order IIR Antiderivative Antialiasing Nonlinear digital circuits and waveshaping are active areas of study,
specifically for what concerns numerical and aliasing issues. In
the past, an effective method was proposed to discretize nonlinear
static functions with reduced aliasing based on the antiderivative of
the nonlinear function. Such a method is based on the continuoustime convolution with an FIR antialiasing filter kernel, such as a
rectangular kernel. These kernels, however, are far from optimal
for the reduction of aliasing. In this paper we introduce the use
of arbitrary IIR rational transfer functions that allow a closer approximation of the ideal antialiasing filter, required in the fictitious continuous-time domain before sampling the nonlinear function output. These allow a higher degree of aliasing reduction and
can be flexibly adjusted to balance performance and computational
cost.
Download An Equivalent Circuit Interpretation of Antiderivative Antialiasing The recently proposed antiderivative antialiasing (ADAA) technique for stateful systems involves two key features: 1) replacing a nonlinearity in a physical model or virtual analog simulation
with an antialiased nonlinear system involving antiderivatives of
the nonlinearity and time delays and 2) introducing a digital filter
in cascade with each original delay in the system. Both of these
features introduce the same delay, which is compensated by adjusting the sampling period. The result is a simulation with reduced
aliasing distortion. In this paper, we study ADAA using equivalent
circuits, answering the question: “Which electrical circuit, discretized using the bilinear transform, yields the ADAA system?”
This gives us a new way of looking at the stability of ADAA and
how introducing extra filtering distorts a system’s response. We
focus on the Wave Digital Filter (WDF) version of this technique.
Download Non-Iterative Schemes for the Simulation of Nonlinear Audio Circuits In this work, a number of numerical schemes are presented in the
context of virtual-analog simulation. The schemes are linearlyimplicit in character, and hence directly solvable without iterative
methods. Schemes of increasing order of accuracy are constructed,
and convergence and stability conditions are proven formally. The
schemes are able to handle stiff problems very efficiently, because
of their fast update, and can be run at higher sample rates to reduce
aliasing. The cases of the diode clipper and ring modulator are
investigated in detail, including several numerical examples.
Download Identification of Nonlinear Circuits as Port-Hamiltonian Systems 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.
Download Applications of Port Hamiltonian Methods to Non-Iterative Stable Simulations of the Korg35 and Moog 4-Pole Vcf This paper presents an application of the port Hamiltonian formalism to the nonlinear simulation of the OTA-based Korg35 filter circuit and the Moog 4-pole ladder filter circuit. Lyapunov analysis is
used with their state-space representations to guarantee zero-input
stability over the range of parameters consistent with the actual
circuits. A zero-input stable non-iterative discrete-time scheme
based on a discrete gradient and a change of state variables is
shown along with numerical simulations. Simulations show behavior consistent with the actual operation of the circuits, e.g.,
self-oscillation, and are found to be stable and have lower computational cost compared to iterative methods.
Download Higher-Order Anti-Derivatives of Band Limited Step Functions for the Design of Radial Filters in Spherical Harmonics Expansions This paper presents a discrete-time model of the spherical harmonics expansion describing a sound field. The so-called radial functions are realized as digital filters, which characterize the spatial
impulse responses of the individual harmonic orders. The filter
coefficients are derived from the analytical expressions of the timedomain radial functions, which have a finite extent in time. Due
to the varying degrees of discontinuities occurring at their edges, a
time-domain sampling of the radial functions gives rise to aliasing.
In order to reduce the aliasing distortion, the discontinuities are replaced with the higher-order anti-derivatives of a band-limited step
function. The improved spectral accuracy is demonstrated by numerical evaluation. The proposed discrete-time sound field model
is applicable in broadband applications such as spatial sound reproduction and active noise control.
Download Practical Virtual Analog Modeling Using Möbius Transforms Möbius transforms provide for the definition of a family of onestep discretization methods offering a framework for alleviating
well-known limitations of common one-step methods, such as the
trapezoidal method, at no cost in model compactness or complexity. In this paper, we extend the existing theory around these methods. Here, we show how it can be applied to common frameworks
used to structure virtual analog models. Then, we propose practical strategies to tune the transform parameters for best simulation
results. Finally, we show how such strategies enable us to formulate much improved non-oversampled virtual analog models for
several historical audio circuits.