Wave field synthesis using fractional order systems and fractional delays

A discretization of the generalized 2.5D wave field synthesis driving functions is proposed in this paper. Time discretization is applied with special attention to prefiltering that involves half-order systems and to delaying that involves fractional-sample delays. Space discretization uses uniformly distributed loudspeakers along arbitrarily shaped contours. Visual and numerical comparisons between continuous and discrete synthesis with line, square and circular arrays are shown. An immersive soundscape composed of nature sounds is reported as example. Simulations have been done with MATLAB and real-time reproduction with Pure Data. Simulations of synthesized plane and spherical wave fields, in the whole listening area, report a percentage discretization error of less than 1%, using a 5 ^th order IIR filter for prefiltering and a 3 ^rd order IIR filter per channel for fractional delaying.