Analysis on the influence of number of loudspeakers on the error in binarual pressure spectra for spatial Ambisonics reproduction

Ambisonics is a series of spatial sound reproduction system with flexible number of loudspeakers. Based on spatial harmonics decomposition and truncation at various orders, it aims at approximate reconstruction of target sound field within a certain region and below a certain frequency limit. The region and frequency limit are determined by spatial sampling theorem of sound field. The present work evaluates the influence of number of loudspeakers on the errors in binaural pressure spectra for spatial Ambisonics reproduction. Binaural pressures for target sound field and Ambisonics reproduction are calculated and normalized square amplitude error in binaural pressures is used as error index. The results indicate that, for each order Ambisonics reproduction, and when the number of loudspeakers exceeds the low limit, increasing the number of loudspeakers reduces, or at least does not increase the errors in binaural pressures. Around the frequency limit given by spatial sampling theorem, the reduction on the errors in binaural pressures by increasing number of loudspeakers is significant. On the other hand, below or above that frequency limit moderately, the reduction is insignificant in terms of auditory perception.