Download HD-AD: A New Approach to Audio Atomic Decomposition with Hyperdimensional Computing In this paper, we approach the problem of atomic decomposition of audio at the symbolic level of atom parameters through the lens of hyperdimensional computing (HDC) – a non-traditional computing paradigm. Existing atomic decomposition algorithms often operate using waveforms from a redundant dictionary of atoms causing them to become increasingly memory/computationally intensive as the signal length grows and/or the atoms become more complicated. We systematically build an atom encoding using vector function architecture (VFA), a field of HDC. We train a neural network encoder on synthetic audio signals to generate these encodings and observe that the network can generalize to real recordings. This system, we call Hyperdimensional Atomic Decomposition (HD-AD), avoids time-domain correlations all together. Because HD-AD scales with the sparsity of the signal, rather than its length in time, atomic decompositions are often produced much faster than real-time.
Download Combined Derivative/Antiderivative Antialiasing Nonlinear systems play an important role in musical signal processing, but their digital implementation suffers from the occurrence of aliasing distortion. Consequently, various aliasing reduction methods have been proposed in the literature. In this work, a novel approach is examined that uses samples of a signal’s derivative in addition to the signal’s samples themselves. This allows some aliasing reduction, but is usually insufficient on its own. However, it can elegantly and fruitfully be combined with antiderivative antialiasing to obtain an effective method. Unfortunately, it still compares unfavorably to oversampled antiderivative antialiasing. It may therefore be regarded as a negative result, but it may hopefully still form a basis for further developments.
Download A Low-Latency Quasi-Linear-Phase Octave Graphic Equalizer This paper proposes a low-latency quasi-linear-phase octave graphic equalizer. The structure is derived from a recent linearphase graphic equalizer based on interpolated finite impulse response (IFIR) filters. The proposed system reduces the total latency of the previous equalizer by implementing a hybrid structure. An infinite impulse response (IIR) shelving filter is used in the structure to implement the first band of the equalizer, whereas the rest of the band filters are realized with the linear-phase FIR structure. The introduction of the IIR filter causes a nonlinear phase response in the low frequencies, but the total latency is reduced by 50% in comparison to the linear-phase equalizer. The proposed graphic equalizer is useful in real-time audio processing, where only little latency is tolerated.
Download Time-Varying Filter Stability and State Matrix Products We show a new sufficient criterion for time-varying digital filter stability: that the matrix norm of the product of state matrices over a certain finite number of time steps is bounded by 1. This extends Laroche’s Criterion 1, which only considered one time step, while hinting at extensions to two time steps. Further extending these results, we also show that there is no intrinsic requirement that filter coefficients be frozen over any time scale, and extend to any dimension a helpful theorem that allows us to avoid explicitly performing eigen- or singular value decompositions in studying the matrix norm. We give a number of case studies on filters known to be time-varying stable, that cannot be proven time-varying stable with the original criterion, where the new criterion succeeds.
Download A General Antialiasing Method for Sine Hard Sync Hard sync is a feature appearing in many analog synthesizers: it consists in retriggering a slave oscillator, regardless of its phase, every time a master oscillator completes its cycle. If this process is naïvely implemented digitally, it is subject to aliasing. While for sawtooth, square, and triangle waves several effective antialiasing methods have been developed, the literature is sparser concerning sine hard sync, arguably because discontinuities of infinite order are introduced which are more difficult to handle. In this paper, we introduce a new antialiasing algorithm for sine hard sync which is obtained by filtering the hard-synced sine with a FIR lowpass kernel, as opposed to existing methods based on the windowed sinc function. We show that our method yields lower computational cost and better aliasing reduction.
Download Fast Temporal Convolutions for Real-Time Audio Signal Processing This paper introduces the possibilities of optimizing neural network convolutional layers for modeling nonlinear audio systems and effects. Enhanced methods for real-time dilated convolutions are presented to achieve faster signal processing times than in previous work. Due to the improved implementation of convolutional layers, a significant decrease in computational requirements was observed and validated on different configurations of single layers with dilated convolutions and WaveNet-style feedforward neural network models. In most cases, equivalent signal processing times were achieved to those using recurrent neural networks with Long Short-Term Memory units and Gated Recurrent Units, which are considered state-of-the-art in the field of black-box virtual analog modeling.
Download Efficient Simulation of the Bowed String in Modal Form The motion of a bowed string is a typical nonlinear phenomenon resulting from a friction force via interaction with the bow. The system can be described using suitable differential equations. Implicit numerical discretisation methods are known to yield energy consistent algorithms, essential to ensure stability of the timestepping schemes. However, reliance on iterative nonlinear root finders carries significant implementation issues. This paper explores a method recently developed which allows nonlinear systems of ordinary differential equations to be solved non-iteratively. Case studies of a mass-spring system and an ideal string coupled with a bow are investigated. Finally, a stiff string with loss is also considered. Combining semi-discretisation and a modal approach results in an algorithm yielding faster than real-time simulation of typical musical strings.
Download Real-Time Implementation of the Dynamic Stiff String Using Finite-Difference Time-Domain Methods and the Dynamic Grid Digital musical instruments based on physical modelling have gained increased popularity over the past years. This is partly due to recent advances in computational power, which allow for their real-time implementation. One of the great potentials for digital musical instruments based on physical models, is that one can go beyond what is physically possible and change properties of the instruments which are static in real life. This paper presents a real-time implementation of the dynamic stiff string using finitedifference time-domain (FDTD) methods. The defining parameters of the string can be varied in real time and change the underlying grid that these methods rely on based on the recently developed dynamic grid method. For most settings, parameter changes are nearly instantaneous and do not cause noticeable artefacts due to changes in the grid. A reliable way to prevent artefacts for all settings is under development.
Download Physical Modeling Using Recurrent Neural Networks with Fast Convolutional Layers Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or partial differential equations, using established techniques. Recent work has applied the techniques of machine-learning to construct such models automatically from data for the case of systems which have lumped states described by scalar values, such as electrical circuits. In this work, we examine how similar techniques are able to construct models of systems which have spatially distributed rather than lumped states. We describe several novel recurrent neural network structures, and show how they can be thought of as an extension of modal techniques. As a proof of concept, we generate synthetic data for three physical systems and show that the proposed network structures can be trained with this data to reproduce the behavior of these systems.
Download Control Parameters for Reed Wind Instruments or Organ Pipes with Reed Induced Flow Sound synthesis of a pipe coupled with a reed requires to finely tune the physical parameters of the underlying model. Although the pipe geometry is often well known, the 1 degree of freedom reed model’s parameters are effective coefficients (mass, section, etc) and are difficult to assess. Studies of this coupled system have essentially focused on models without the reed induced flow, and have exhibited two dimensionless parameters γ and ζ, which respectively describe the ratio between feeding pressure and closing reed pressure, and a dimensionless opening of the reed at rest. Including the reed flow in the model, then performing a scaling of the equations, leads to a new third dimensionless quantity that we will call κ. Varying the reed frequency with constant (γ, ζ, κ) on different pipe dimensions shows a certain stability of the model once put under this form. Using a real-time sound synthesis tool, the parameter space (γ, ζ, κ) is explored while the damping of the reed is also varied.