A digital-filter model for simulating sound absorption in the air

Absorption in air is often overlooked in acoustic propagation simulations, largely due to the lack of low-complexity, valid, and robust modelling techniques. This paper proposes modelling air absorption using a third-order digital filter whose coefficients are derived analytically from the propagation conditions (temperature, pressure, relative humidity, and propagation distance) and the sampling frequency. The proposed filters closely approximate the absorption model specified in the ISO 9613 standard [(1997). 9613-1, International Standards Organization, Geneva, Switzerland]. Errors remain below 50% for 95% of the frequency spectrum between 20 Hz and 20 kHz for propagation distances of up to 25 m, across atmospheric conditions spanning temperatures from -20 °C to 50 °C, relative humidity from 0% to 100%, and pressures from 97 300 Pa to 104 700 Pa. Although accuracy decreases with increasing distance, similar levels are preserved for propagation distances of up to 100 m when the temperature is below 20 °C. The filters are minimum-phase, enabling not only low-cost simulation of air absorption but also stable inverse filtering to remove air-absorption effects from measured acoustic impulse responses.