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 Large stencil operations for GPU-based 3-D acoustics simulations Stencil operations are often a key component when performing acoustics simulations, for which the specific choice of implementation can have a significant effect on both accuracy and computational performance. This paper presents a detailed investigation of computational performance for GPU-based stencil operations in two-step finite difference schemes, using stencils of varying shape and size (ranging from seven to more than 450 points in size). Using an Nvidia K20 GPU, it is found that as the stencil size increases, compute times increase less than that naively expected by considering only the number of computational operations involved, because performance is instead determined by data transfer times throughout the GPU memory architecture. With regards to the effects of stencil shape, performance obtained with stencils that are compact in space is mainly due to efficient use of the read-only data (texture) cache on the K20, and performance obtained with standard high-order stencils is due to increased memory bandwidth usage, compensating for lower cache hit rates. Also in this study, a brief comparison is made with performance results from a related, recent study that used a shared memory approach on a GTX 670 GPU device. It is found that by making efficient use of a GTX 660Ti GPU—whose computational performance is generally lower than that of a GTX 670—similar or better performance to those results can be achieved without the use of shared memory.
Download Sample Rate Independent Recurrent Neural Networks for Audio Effects Processing In recent years, machine learning approaches to modelling guitar amplifiers and effects pedals have been widely investigated and have become standard practice in some consumer products. In particular, recurrent neural networks (RNNs) are a popular choice for modelling non-linear devices such as vacuum tube amplifiers and distortion circuitry. One limitation of such models is that they are trained on audio at a specific sample rate and therefore give unreliable results when operating at another rate. Here, we investigate several methods of modifying RNN structures to make them approximately sample rate independent, with a focus on oversampling. In the case of integer oversampling, we demonstrate that a previously proposed delay-based approach provides high fidelity sample rate conversion whilst additionally reducing aliasing. For non-integer sample rate adjustment, we propose two novel methods and show that one of these, based on cubic Lagrange interpolation of a delay-line, provides a significant improvement over existing methods. To our knowledge, this work provides the first in-depth study into this problem.
Download Numerical Simulation of Spring Reverberation Virtual analog modeling of spring reverberation presents a challenging problem to the algorithm designer, regardless of the particular strategy employed. The difficulties lie in the behaviour of the helical spring, which, due to its inherent curvature, shows characteristics of both coherent and dispersive wave propagation. Though it is possible to emulate such effects in an efficient manner using audio signal processing constructs such as delay lines (for coherent wave propagation) and chains of allpass filters (for dispersive wave propagation), another approach is to make use of direct numerical simulation techniques, such as the finite difference time domain method (FDTD) in order to solve the equations of motion directly. Such an approach, though more computationally intensive, allows a closer link with the underlying model system— and yet, there are severe numerical difficulties associated with such designs, and in particular anomalous numerical dispersion, requiring some care at the design stage. In this paper, a complete model of helical spring vibration is presented; dispersion analysis from an audio perspective allows for model simplification. A detailed description of novel FDTD designs follows, with special attention is paid to issues such as numerical stability, loss modeling, numerical boundary conditions, and computational complexity. Simulation results are presented.
Download Differentiable All-Pole Filters for Time-Varying Audio Systems Infinite impulse response filters are an essential building block of many time-varying audio systems, such as audio effects and synthesisers. However, their recursive structure impedes end-toend training of these systems using automatic differentiation. Although non-recursive filter approximations like frequency sampling and frame-based processing have been proposed and widely used in previous works, they cannot accurately reflect the gradient of the original system. We alleviate this difficulty by reexpressing a time-varying all-pole filter to backpropagate the gradients through itself, so the filter implementation is not bound to the technical limitations of automatic differentiation frameworks. This implementation can be employed within audio systems containing filters with poles for efficient gradient evaluation. We demonstrate its training efficiency and expressive capabilities for modelling real-world dynamic audio systems on a phaser, time-varying subtractive synthesiser, and feed-forward compressor. We make our code and audio samples available and provide the trained audio effect and synth models in a VST plugin1 .