Andrew S. Allen

Aerophones in flatland: interactive wave simulation of wind instruments

We present the first real-time technique to synthesize full-bandwidth sounds for 2D virtual wind instruments. A novel interactive wave solver is proposed that synthesizes audio at 128,000Hz on commodity graphics cards. Simulating the wave equation captures the resonant and radiative properties of the instrument body automatically. We show that a variety of existing non-linear excitation mechanisms such as reed or lips can be successfully coupled to the instruments 2D wave field. Virtual musical performances can be created by mapping user inputs to control geometric features of the instrument body, such as tone holes, and modifying parameters of the excitation model, such as blowing pressure. Field visualizations are also produced. Our technique promotes experimentation by providing instant audio-visual feedback from interactive virtual designs. To allow artifact-free audio despite dynamic geometric modification, we present a novel time-varying Perfectly Matched Layer formulation that yields smooth, natural-sounding transitions between notes. We find that visco-thermal wall losses are crucial for musical sound in 2D simulations and propose a practical approximation. Weak non-linearity at high amplitudes is incorporated to improve the sound quality of brass instruments.

Numerical wave simulation for interactive audio-visual applications

Sound is an integral part of many interactive applications, such as 3D computer games. The generality and complexity of the simulated domains makes wave simulation a natural fit. The opposing goals of real-time execution and compute intensiveness of wave simulation provide a rich ground for designing novel computational methods. Two instances of such audio-visual interactive techniques will be discussed. The first technique employs precomputed wave simulation for providing acoustic effects in computer games. Time-domain 3D simulation is performed from many prospective player positions, resulting in a 7D field containing billions of acoustic responses. Perceptual encoding is then performed to drastically reduce memory requirements. Interactive motion of player and sources in the game can then be accommodated via quickly decoding and auralizing the pre-calculated wave effects. The second technique explores the limits of real-time parallel numerical acoustic computation on todays desktop graphics cards. The...

Aural ordinary differential equations: Methods for generating audio from mass-spring systems

In this article, I focus on the harmonic oscillator as a model by which to compare several numerical methods for solving ordinary differential equations (ODEs). I first define the simple harmonic oscillator as an ODE and then extend its behavior by adding additional forces and physical properties to the equation. I next proceed to discuss computational methods for solving ODEs and use the oscillator model as a means of evaluating and comparing three methods in terms of their stability, drift, and computational costs when working at the audio-rate.