Air Absorption Filtering Method Based on Approximate Green's Function for Stokes' Equation

Abstract

Air absorption effects lead to significant attenuation in high frequencies over long distances and this is critical to model in wide-band virtual acoustic simulations. Air absorption is commonly modelled using filter banks applied to an impulse response or to individual impulse events (rays or image sources) arriving at a receiver. Such filter banks require non-trivial fitting to air absorption attenuation curves, as a function of time or distance, in the case of IIR approximations' or may suffer from overlap-add artefacts in the case of FIR approximations. In this study, a filter method is presented which avoids the aforementioned issues. The proposed approach relies on a time-varying diffusion kernel that is found in an approximate Green's function solution to Stokes' equation in free space. This kernel acts as a low-pass filter that is parametrised by physical constants, and can be applied to an impulse response using time-varying convolution. Numerical examples are presented demonstrating the utility of this approach for adding air absorption effects to room impulse responses simulated using geometrical acoustics or wave-based methods.