![]() At θ S B = π + θ s, the shadow boundary (SB) separates the shadow zone where the GA direct sound component disappears from the “illuminated” zone. θ b = θ r − θ s denotes the bending (deflection) angle of the sound path. A point source is assumed to be located at an angle θ s from the (closer) wedge plane P e, s while the receiver is located at an angle θ r from the wedge plane P e, s. A cylindrical coordinate system with the z-axis along the edge is assumed. Filter representation of diffraction at infinite wedgesĪ rigid infinite wedge is considered, formed by two intersecting planes at an open angle θ w as depicted in Fig. Based on the filter representation for infinite wedges, finite wedges are described by truncation in the time domain or convolution with the according sinc function in the frequency domain. Expressions for the filter transfer functions and the impulse responses are provided. The suggested filter representation can be extended by an alternative asymptotic low-frequency filter function to approximate the exact BTMS solution, helping to interconnect the existing solutions. ![]() It is shown that the cutoff frequencies and gains of the same underlying lowpass filter function can be derived from the asymptotic solution for diffraction of Pierce (1974, 2019) and Kouyoumjian and Pathak (1974). Wedge diffraction is described as superposition of (up to four) fractional half-order lowpass filters, representing the diffracted incident and reflected sound field. Here, a unified filter representation of the singly diffracted sound field by an arbitrary wedge is suggested. Parametric filter approximations of diffraction have been optimized in Pulkki and Svensson (2019) using machine learning, and have been heuristically derived using geometric parameters for a diffraction lowpass filter in Kirsch and Ewert (2021), also with restrictions to the shadow zone. With considerable computation time spent on diffraction path finding, existing approximations for VAEs typically use filters derived by evaluating diffraction solutions at relatively low spectral resolution and restriction to infinite wedges in the shadow zone (e.g., Schissler et al., 2021) or from a coarse approximation of prototypical object shapes (e.g., Pisha et al., 2020). Several approximations have been suggested, e.g., using empirically based simplifications ( Maekawa, 1968), for the required Fresnel terms in UTD ( Kawai, 1981), for the secondary source model (e.g., Calamia and Svensson, 2006) in the context of a directive line source model (e.g., Menounou and Nikolaou, 2017), or for half-planes ( Ouis, 2019). (2009) use line integrals along the physical edge based on the concept of secondary sources located along the edge, particularly suited for handling finite edges. A reformulation in the frequency domain was presented in Svensson et al. An exact time-domain solution was suggested by Biot and Tolstoy (1957) and extended by Medwin (1981) and Svensson et al. The uniform theory of diffraction (UTD Kouyoumjian and Pathak, 1974) has been established as an asymptotic high-frequency solution for diffraction of electromagnetic waves and similar solutions for acoustic diffraction have been derived (e.g., Pierce, 1974). Keller (1962) coined the concept of edge diffracted rays in the geometrical theory of diffraction (GTD), considering the incident and reflected diffracted field at straight and curved edges. To account for edge diffraction, several exact and asymptotic solutions in the frequency and time domain exist.
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