Filter-based first- and higher-order diffraction modeling for geometrical acoustics

Geometrical acoustics (GA) offers a high computational efficiency, as required for real-time renderings of complex acoustic environments with applications in, e.g., hearing research, architectural planning, and entertainment. However, the assumed ray-like sound propagation does not account for perceptually relevant effects of diffraction. In indoor environments, diffraction at finite objects and apertures such as tables, music stands, and doors is of interest for computationally efficient rendering. Outdoors, buildings and barriers are relevant. Here, we extend the recent physically-based universal diffraction filter approximation (UDFA) for GA to approximate spectral effects of higher-order diffraction and apply it to a flat finite object and a double edge. At low frequencies, such effects predominantly occur when sound is diffracted repeatedly at the edges of a finite object, and at high frequencies when sound is propagating around subsequent edges of, e.g., buildings or sound barriers. In contrast to existing methods, the suggested filter approaches and topology offer spatially smooth infinite impulse response implementation for modelling higher-order diffraction at flat objects for arbitrary geometrical arrangements. For double diffraction at a three-sided barrier, errors are considerably decreased in comparison to a state-of-the-art sequential approach. Both suggested methods are computationally highly efficient and scalable depending on the desired accuracy.