Filter-based solutions for finite and infinite edge diffraction

Abstract

Sound diffraction occurs at (building) corners, objects and openings, prominently affecting occluded and reflected sounds. Here, a physically-based, parametric filter model for diffraction at arbitrary wedges is presented. The model connects existing high-frequency asymptotic and exact solutions in geometrical acoustics using up to four half-order low-pass filters. Compact expressions for the transfer function and impulse response of the singly diffracted field are derived, with errors below 0.1 dB. A filter modification is suggested to account for the exact solution at low frequencies. The filter solution is further simplified to approximate the spectral effects of diffraction from finite wedges and objects composed thereof, referred to as universal diffraction filter approximation (UDFA). A computationally highly-efficient recursive filter implementation is presented and it is demonstrated that diffraction from flat finite objects like plates or apertures can be closely approximated. To account for effects of higher-order diffraction at the object, a heuristic filter extension is suggested. The presented filter-based diffraction solution is suited for the prediction and simulation of sound propagation including non-specular reflections in architectural acoustics. For virtual acoustics, UDFA provides an efficient and accurate approximation of edge diffraction to account for perceptually relevant frequency-dependent attenuation, extendable to arbitrary objects.