Low-Order Filter Approximation of Diffraction for Virtual Acoustics

Geometrical acoustics can be used to create virtual acoustic environments at low computational cost, disregarding diffraction phenomena based on the wave properties of sound. For the auralization of indoor and outdoor scenarios, a highly relevant case of diffraction occurs for sounds behind an exterior corner or barrier where sounds “bend” around the edge into the “shadow” region. In many cases, the edge can be considered infinite to a first approximation for which analytic solutions exist. However, for realtime, interactive simulation of sound diffraction in virtual acoustics, computationally efficient, time-domain digital filter approaches are desirable, suited to account for the most prominent and perceptually relevant effect of frequency-dependent attenuation. This contribution suggests the design of highly -efficient, recursive filters to approximate effects of diffraction in the shadow region of an infinite edge: i) In comparison to the analytical solution, it is shown that the effect of diffraction can be generally well approximated by a fractional half-order low-pass filter with a cutoff frequency depending on the source and receiver position in relation to the edge. ii) A low-order recursive filter design ensuring smooth transition and interpolation of filter coefficients for dynamically changing geometric conditions is derived and compared to the analytical solution.