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 frequencydependent attenuation. Geometrical acoustics (GA) have become a de-facto standard for 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 firstorder 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.

Filter-based First- and Higher-Order Diffraction Modeling

“…The distances between source and receiver and the apex point 𝑧 a are 𝑑 𝑠 and 𝑑 𝑟 , respectively. Based on Ewert [17], UDFA [18] describes the diffracted sound by the superposition of a scalable number of one to four modified fractional-order low-pass filters. For general virtual acoustics applications, using two terms is recommended, where the (infinite edge) cutoff frequencies for the low-pass filters are derived from the geometry at the wedge as…”

“…Here, 𝛼 = 0.5 is the fractional filter order and the parameters 𝑏 = 1.44, 𝑄 = 0.2, and 𝑟 = 1.6, provide a smooth roll-off around the cutoff frequency. For a detailed theoretical description, see [17] and for the finite wedge approximation method and IIR implementation, see [18]. Diffracted sound is implemented using the serial shelving filter design described in [18], and a separate phase-inversion stage at the output of each filter stage.…”

“…For a detailed theoretical description, see [17] and for the finite wedge approximation method and IIR implementation, see [18]. Diffracted sound is implemented using the serial shelving filter design described in [18], and a separate phase-inversion stage at the output of each filter stage. Here, two parallel diffraction filters with the transfer functions 𝐻 diff,1 and 𝐻 diff,2 are used (two-term solution from [18]).…”

“…All above diffraction solutions are computationally quite involved and are not directly applicable for real-time VAEs, particularly considering HO diffraction. Recently, filter-based diffraction solutions were proposed [16,17,18], offering a physically-based, computationally highly-efficient method to model diffraction from arbitrary infinite and finite wedges. Ewert [17] derived filter representations of the asymptotic solutions [6,7] and an approximation of BTMS in both frequency and time domain, based on modified fractional-order transfer functions and the corresponding impulse response.…”

“…Diffracted sound is parametrized by cutoff frequencies derived from the geometry at the edge. The universal diffraction filter approximation (UDFA; [18]) introduces simplifications for finite edges and proposes a recursive filter design. Furthermore, it was demonstrated that diffraction by flat, rectangular plate can be characterized by superimposing the four individually filtered edge paths.…”