Discrete driving functions for horizontal reproduction using Wave Field Synthesis and Higher Order Ambisonics

Practical implementations of physics-based spatial sound reproduction techniques, such as Wave Field Synthesis (WFS) and Higher Order Ambisonics (HOA), require real-time filtering, scaling and delaying operations on the audio signal to be spatialized. These operations form the so-called loudspeaker's driving function. This paper describes a discretization method to obtain rational representations, in the unit circle of the z-plane, of the continuous 2.5D-WFS and 2D-HOA driving functions for horizontal reproduction. Visual and numerical comparisons between continuous and discrete driving functions, and between continuous and discrete sound pressure fields, synthesized with circular loudspeaker arrays, are shown. Percentage discretization errors, in the reproducible frequency range and in the whole listening area, are on the order of 1%. A methodology for immersive soundscapes reconstruction composed with nature sounds is also reported as a practical application.