Designing Practical Filters For Sound Field Reconstruction

Multichannel sound field reproduction techniques, such as Wave Field Synthesis (WFS) and Sound Field Reconstruction (SFR), define loudspeaker filters in the frequency domain. However, in order to use these techniques in practical systems, one needs to convert these frequency-domain characteristics to practical and efficient time-domain digital filters. Additional limitation of SFR comes from the fact that it uses a numerical matrix pseudoinversion procedure, where the obtained filters are sensitive to numerical errors when the system matrix has a high condition number. This paper describes physically-motivated modifications of the SFR approach that allow for mitigating conditioning problems and frequency-domain loudspeaker filter smoothing that allows for designing short time-domain filters while maintaining high sound field reproduction accuracy. It also provides comparisons of sound field reproduction accuracy of WFS and SFR using the obtained discrete-time filters.