Local Time-domain Spherical Harmonic Spatial Encoding for Wave-based Acoustic Simulation

Volumetric time-domain simulation methods, such as the finite difference time domain method, allow for a fine-grained representation of the dynamics of the acoustic field. A key feature of such methods is complete access to the computed field, normally represented over a Cartesian grid. Simple solutions to the problem of extracting spatially encoded signals, necessary in virtual acoustics applications, result. In this letter, a simple time-domain representation of spatially encoded spherical harmonic signals is written directly in terms of spatial derivatives of the acoustic field at the receiver location. In a discrete setting, encoded signals may be obtained, at very low computational cost and latency, using local approximations with minimal number of grid points, and avoiding large convolutions and frequency-domain block processing of previous approaches. Numerical results illustrating receiver directivity and computed time-domain responses are presented, as well as numerical solution drift associated withrepeated time integration.Peer reviewe

Filter design for real-time ambisonics encoding during wave-based acoustic simulations

The ambisonics format is a powerful audio tool designed for spatial encoding of the pressure field. An under-exploited feature of this format is that it can be directly extracted from virtual acoustics simulations. Finite Difference Time Domain (FDTD) simulations are particularly adapted as they simplify greatly the problem of extracting spatially-encoded signals, and enable real-time processing of the simulated pressure field. In this short contribution, we first write a time domain representation of the ambisonics channels, in terms of spatial derivatives of the acoustic field at the receiver location, and formulated as a set of ordinary differential equations. We show that in general, the natural corresponding discrete recursive integration yields a prohibitive polynomial drift in time. We then describe a real-time filtering strategy which stabilizes this numerical integration; in the discrete-time setting of FDTD simulations, this real-time filtering process features very low computational costs, avoiding the latency associated with large convolutions and frequency-domain block processing of previous approaches.publishedVersio

Local directional source modeling in wave-based acoustic simulation

Time-domain wave-based simulation approaches such as the finite difference time domain (FDTD) method allow for a complete solution to the problem of virtual acoustics over the entire frequency range, in contrast with the methods of geometric acoustics which are valid in the limit of high frequencies. They also allow for flexible modelling of sources and receivers, due to the inherently local nature of the computation, and complete access to the computed acoustic field over an enclosure. In this paper, a method for the emulation of sources of arbitrary directivity is presented, framed directly as an inhomogeneous wave equation. The additional terms in the wave equation take the form of Dirac delta functions and their distributional derivatives, and collections of such terms may be associated directly with an expansion of source directivity in terms of spherical harmonics. The local nature of the model implies a locally-defined efficient computational approach for wave-based methods defined over a spatial grid. Numerical results are presented