Download Antiderivative Antialiasing in Nonlinear Wave Digital Filters A major problem in the emulation of discrete-time nonlinear systems, such as those encountered in Virtual Analog modeling, is
aliasing distortion. A trivial approach to reduce aliasing is oversampling. However, this solution may be too computationally demanding for real-time applications. More advanced techniques
to suppress aliased components are arbitrary-order Antiderivative
Antialiasing (ADAA) methods that approximate the reference nonlinear function using a combination of its antiderivatives of different orders. While in its original formulation it is applied only
to memoryless systems, recently, the applicability of first-order
ADAA has been extended to stateful systems employing their statespace description. This paper presents an alternative formulation
that successfully applies arbitrary-order ADAA methods to Wave
Digital Filter models of dynamic circuits with one nonlinear element. It is shown that the proposed approach allows us to design
ADAA models of the nonlinear elements in a fully local and modular fashion, independently of the considered reference circuit. Further peculiar features of the proposed approach, along with two
examples of applications, are discussed.
Download Moog Ladder Filter Generalizations Based on State Variable Filters We propose a new style of continuous-time filter design composed
of a cascade of 2nd-order state variable filters (SVFs) and a global
feedback path. This family of filters is parameterized by the SVF
cutoff frequencies and resonances, as well as the global feedback
amount. For the case of two identical SVFs in cascade and a specific value of the SVF resonance, the proposed design reduces to
the well-known Moog ladder filter. For another resonance value,
it approximates the Octave CAT filter. The resonance parameter
can be used to create new filters as well. We study the pole loci
and transfer functions of the SVF building block and entire filter.
We focus in particular on the effect of the proposed parameterization on important aspects of the filter’s response, including the
passband gain and cutoff frequency error. We also present the first
in-depth study of the Octave CAT filter circuit.
Download Fully-Implicit Algebro-Differential Parametrization of Circuits This paper is concerned with the conception of methods tailored
for the numerical simulation of power-balanced systems that are
well-posed but implicitly described. The motivation is threefold:
some electronic components (such as the ideal diode) can only
be implicitly described, arbitrary connection of components can
lead to implicit topological constraints, finally stable discretization
schemes also lead to implicit algebraic equations.
In this paper we start from the representation of circuits using a
power-balanced Kirchhoff-Dirac structure, electronic components
are described by a local state that is observed through a pair of
power-conjugated algebro-differential operators (V, I) to yield the
branch voltages and currents, the arc length is used to parametrize
switching and non-Lipschitz components, and a power balanced
functional time-discretization is proposed. Finally, the method is
illustrated on two simple but non-trivial examples.
Download Virtual Bass System With Fuzzy Separation of Tones and Transients A virtual bass system creates an impression of bass perception
in sound systems with weak low-frequency reproduction, which
is typical of small loudspeakers. Virtual bass systems extend the
bandwidth of the low-frequency audio content using either a nonlinear function or a phase vocoder, and add the processed signal
to the reproduced sound. Hybrid systems separate transients and
steady-state sounds, which are processed separately. It is still challenging to reach a good sound quality using a virtual bass system.
This paper proposes a novel method, which separates the tonal,
transient, and noisy parts of the audio signal in a fuzzy way, and
then processes only the transients and tones. Those upper harmonics, which can be detected above the cutoff frequency, are boosted
using timbre-matched weights, but missing upper harmonics are
generated to assist the missing fundamental phenomenon. Listening test results show that the proposed algorithm outperforms selected previous methods in terms of perceived bass sound quality.
The proposed method can enhance the bass sound perception of
small loudspeakers, such as those used in laptop computers and
mobile devices.
Download Stable Structures for Nonlinear Biquad Filters Biquad filters are a common tool for filter design. In this writing,
we develop two structures for creating biquad filters with nonlinear elements. We provide conditions for the guaranteed stability of
the nonlinear filters, and derive expressions for instantaneous pole
analysis. Finally, we examine example filters built with these nonlinear structures, and show how the first nonlinear structure can be
used in the context of analog modelling.
Download Optimization of Cascaded Parametric Peak and Shelving Filters With Backpropagation Algorithm Peak and shelving filters are parametric infinite impulse response
filters which are used for amplifying or attenuating a certain frequency band. Shelving filters are parametrized by their cut-off frequency and gain, and peak filters by center frequency, bandwidth
and gain. Such filters can be cascaded in order to perform audio processing tasks like equalization, spectral shaping and modelling of complex transfer functions. Such a filter cascade allows
independent optimization of the mentioned parameters of each filter. For this purpose, a novel approach is proposed for deriving
the necessary local gradients with respect to the control parameters and for applying the instantaneous backpropagation algorithm
to deduce the gradient flow through a cascaded structure. Additionally, the performance of such a filter cascade adapted with the
proposed method, is exhibited for head-related transfer function
modelling, as an example application.
Download Bistable Digital Audio Effect A mechanical system is said to be bistable when its moving parts
can rest at two equilibrium positions. The aim of this work is to
model the vibration behaviour of a bistable system and use it to
create a sound effect, taking advantage of the nonlinearities that
characterize such systems. The velocity signal of the bistable system excited by an audio signal is the output of the digital effect.
The latter is coded in C++ language and compiled into VST3 format that can be run as an audio plugin within most of the commercial digital audio workstation software in the market and as a
standalone application. A Web Audio API demonstration is also
available online as a support material.
Download Flexible Framework for Audio Restoration The paper presents a unified, flexible framework for the tasks
of audio inpainting, declipping, and dequantization. The concept is
further extended to cover analogous degradation models in a transformed domain, e.g. quantization of the signal’s time-frequency
coefficients. The task of reconstructing an audio signal from degraded observations in two different domains is formulated as an
inverse problem, and several algorithmic solutions are developed.
The viability of the presented concept is demonstrated on an example where audio reconstruction from partial and quantized observations of both the time-domain signal and its time-frequency
coefficients is carried out.
Download GPGPU Patterns for Serial and Parallel Audio Effects Modern commodity GPUs offer high numerical throughput per
unit of cost, but often sit idle during audio workstation tasks. Various researches in the field have shown that GPUs excel at tasks
such as Finite-Difference Time-Domain simulation and wavefield
synthesis. Concrete implementations of several such projects are
available for use.
Benchmarks and use cases generally concentrate on running
one project on a GPU. Running multiple such projects simultaneously is less common, and reduces throughput. In this work
we list some concerns when running multiple heterogeneous tasks
on the GPU. We apply optimization strategies detailed in developer documentation and commercial CUDA literature, and show
results through the lens of real-time audio tasks. We benchmark
the cases of (i) a homogeneous effect chain made of previously
separate effects, and (ii) a synthesizer with distinct, parallelizable
sound generators.
Download Practical Linear and Exponential Frequency Modulation for Digital Music Synthesis This paper explores Frequency Modulation (FM) for use in music synthesis. We take an in-depth look at Linear FM, LinearThrough-Zero FM, Phase Modulation (PM) and Exponential
FM, and discuss their pros and cons for sound synthesis in a digital system. In the process we derive some useful formulas and
discuss their implementation details. In particular we derive analytic expressions for DC correcting Exponential FM, and make it
match the modulation depth of Linear FM. Finally, we review
practical antialiasing solutions.