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

The ambisonics format is a powerful audio tool de-signed for spatial encoding of the pressure field. Anunder-exploited feature of this format is that it can bedirectly extracted from virtual acoustics simulations.Finite Difference Time Domain (FDTD) simulations areparticularly adapted as they simplify greatly the prob-lem of extracting spatially-encoded signals, and enablereal-time processing of the simulated pressure field. Inthis short contribution, we first write a time domainrepresentation of the ambisonics channels, in terms ofspatial derivatives of the acoustic field at the receiver lo-cation, and formulated as a set of ordinary differentialequations. We show that in general, the natural cor-responding discrete recursive integration yields a pro-hibitive polynomial drift in time. We then describe areal-time filtering strategy which stabilizes this numer-ical integration; in the discrete-time setting of FDTDsimulations, this real-time filtering process featuresvery low computational costs, avoiding the latency as-sociated with large convolutions and frequency-domainblock processing of previous approaches.