A Universal Filter Approximation of Edge Diffraction for Geometrical Acoustics

Abstract

Sound propagation in urban and indoor environments often involves diffraction at corners, finite objects and openings, resulting in perceptually relevant frequency-dependent attenuation. Geometrical acoustics (GA) have become a de-facto standard for the prediction and simulation of sound propagation and real-time virtual acoustics, including effects of edge diffraction. However, methods to account for edge diffraction often assume infinite edges, such as the uniform theory of diffraction, or are computationally involved, such as the Biot-Tolstoy-Medwin-Svensson (BTMS) method. Particularly for interactive auralization, an efficient approximation of edge diffraction is desirable. Here, an extension of GA to account for diffraction with simple-to-derive parameters and a time-domain recursive filter implementation is suggested. This universal diffraction filter approximation (UDFA) describes diffraction from infinite and finite wedges using a combination of first-order and (fractional) half-order low-pass filters to account for the frequency-dependent attenuation of the diffracted incident and reflected sound field. The physically-based UDFA exactly matches asymptotic solutions for infinite wedges and provides approximations for finite wedges. It is demonstrated that first-order diffraction from flat finite objects like a plate or an aperture can be described by combining the filters for each edge. To account for effects of higher-order diffraction, an additional heuristic filter extension is suggested.