Efficient implementation of the spectral division method for arbitrary virtual sound fields

The Spectral Division Method is an analytic approach for sound field synthesis that determines the loudspeaker driving function in the wavenumber domain. Compact expressions for the driving function in time-frequency domain or in time domain can only be determined for a low number of special cases. Generally, the involved spatial Fourier transforms have to be evaluated numerically. We present a detailed description of the computational procedure and minimize the number of required computations by exploiting the following two aspects: 1) The interval for the spatial sampling of the virtual sound field can be selected for each time-frequency bin, whereby low time-frequency bins can be sampled more coarsely, and 2) the driving function only needs to be evaluated at the locations of the loudspeakers of a given array. The inverse spatial Fourier transform is therefore not required to be evaluated at all initial spatial sampling points but only at those locations that coincide with loudspeakers.