A discretization of the wave field synthesis method for auralization of natural sounds

A complete description of the implementation of an immersive soundscape is proposed in this document. It begins with the time-discretization of the continuous wave field synthesis method for arbitrary contours, with special attention to the prefilter stage that involves a fractional order system. On this stage, the Al-alaoui discretization, the Grünwald-Letnikov approach for fractional expansion, and the Shank least squares approximation method to compute the zero-pole filter that generates the fractional system are described. The document goes on to explain the rendering of background and foreground sounds, using respectively plane and spherical wave models. The simulations of sound pressure fields inside the listening area also shown. Finally, simulations of a real case report a discretization percentage error around 1%, using 24 loudspeakers and a 5th order IIR pre-filter per channel.