Download Performance Portability for Room Acoustics Simulations Numerical modelling of the 3-D wave equation can result in very accurate virtual auralisation, at the expense of computational cost. Implementations targeting modern highly-parallel processors such as NVIDIA GPUs (Graphics Processing Units) are known to be very effective, but are tied to the specific hardware for which they are developed. In this paper, we investigate extending the portability of these models to a wider range of architectures without the loss of performance. We show that, through development of portable frameworks, we can achieve acoustic simulation software that can target other devices in addition to NVIDIA GPUs, such as AMD GPUs, Intel Xeon Phi many-core CPUs and traditional Intel multi-core CPUs. The memory bandwidth offered by each architecture is key to achievable performance, and as such we observe high performance on AMD as well as NVIDIA GPUs (where high performance is achievable even on consumer-class variants despite their lower floating point capability), whilst retaining portability to the other less-performant architectures.
Download Differentiable grey-box modelling of phaser effects using frame-based spectral processing Machine learning approaches to modelling analog audio effects have seen intensive investigation in recent years, particularly in the context of non-linear time-invariant effects such as guitar amplifiers. For modulation effects such as phasers, however, new challenges emerge due to the presence of the low-frequency oscillator which controls the slowly time-varying nature of the effect. Existing approaches have either required foreknowledge of this control signal, or have been non-causal in implementation. This work presents a differentiable digital signal processing approach to modelling phaser effects in which the underlying control signal and time-varying spectral response of the effect are jointly learned. The proposed model processes audio in short frames to implement a time-varying filter in the frequency domain, with a transfer function based on typical analog phaser circuit topology. We show that the model can be trained to emulate an analog reference device, while retaining interpretable and adjustable parameters. The frame duration is an important hyper-parameter of the proposed model, so an investigation was carried out into its effect on model accuracy. The optimal frame length depends on both the rate and transient decay-time of the target effect, but the frame length can be altered at inference time without a significant change in accuracy.
Download More Modal Fun - “Forced Vibration” at One Point The question, if a vibrating object can be forced to follow a given movement profile at one point forms a case of an inverse problem. It is shown that for the specific setting of an object described by modal data, this question may be solved by a newly developed method. The new technique has several strengths, such as allowing to compute modal data for the constrained scenario and forming a basis for precise and stable simulations. The latter potential is shown at a short example, a stiff string being hammered against a fixed board by a hammer of infinite mass.
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 On Iterative Solutions for Numerical Collision Models Nonlinear interactions between different parts of musical instruments present several challenges regarding the formulation of reliable and efficient numerical sound synthesis models. This paper focuses on a numerical collision model that incorporates impact damping. The proposed energy-based approach involves an iterative solver for the solution of the nonlinear system equations. In order to ensure the efficiency of the presented algorithm a bound is derived for the maximum number of iterations required for convergence. Numerical results demonstrate energy conservation as well as convergence within a small number of iterations, which is usually much lower than the predicted bound. Finally, an application to music acoustics, involving a clarinet simulation, shows that including a loss mechanism during collisions may have a significant effect on sound production.
Download Digitizing the Schumann PLL Analog Harmonizer The Schumann Electronics PLL is a guitar effect that uses hardwarebased processing of one-bit digital signals, with op-amp saturation and CMOS control systems used to generate multiple square waves derived from the frequency of the input signal. The effect may be simulated in the digital domain by cascading stages of statespace virtual analog modeling and algorithmic approximations of CMOS integrated circuits. Phase-locked loops, decade counters, and Schmitt trigger inverters are modeled using logic algorithms, allowing for the comparable digital implementation of the Schumann PLL. Simulation results are presented.
Download Fourth-Order and Optimised Finite Difference Schemes for the 2-D Wave Equation This paper investigates some fourth-order accurate explicit finite difference schemes for the 2-D wave equation obtained using 13-, 17-, 21-, and 25-point discrete Laplacians. Optimisation is conducted in order to minimise numerical dispersion and computational costs. New schemes are presented that are more computationally efficient than nine-point explicit schemes at maintaining less than one percent wave speed error up to some critical frequency. Simulation results are presented.
Download A Modal Approach to the Numerical Simulation of a String Vibrating Against an Obstacle: Applications to Sound Synthesis A number of musical instruments (electric basses, tanpuras, sitars...) have a particular timbre due to the contact between a vibrating string and an obstacle. In order to simulate the motion of such a string with the purpose of sound synthesis, various technical issues have to be resolved. First, the contact phenomenon, inherently nonlinear and producing high frequency components, must be described in a numerical manner that ensures stability. Second, as a key ingredient for sound perception, a fine-grained frequencydependent description of losses is necessary. In this study, a new conservative scheme based on a modal representation of the displacement is presented, allowing the simulation of a stiff, damped string vibrating against an obstacle with an arbitrary geometry. In this context, damping parameters together with eigenfrequencies of the system can be adjusted individually, allowing for complete control over loss characteristics. Two cases are then numerically investigated: a point obstacle located in the vicinity of the boundary, mimicking the sound of the tanpura, and then a parabolic obstacle for the sound synthesis of the sitar.
Download The wave digital reed: A passive formulation In this short paper, we address the numerical simulation of the single reed excitation mechanism. In particular, we discuss a formalism for approaching the lumped nonlinearity inherent in such a model using a circuit model and the application of wave digital filters (WDFs), which are of interest in that they allow simple stability verification, a property which is not generally guaranteed if one employs straightforward numerical methods. We present first a standard reed model, then its circuit representation, then finally the associated wave digital network. We then enter into some implementation issues, such as the solution of nonlinear algebraic equations, and the removal of delay-free loops, and present simulation results.