Analysis and evaluation of stereophonic and multichannel sound reproduction based on the theorem of sound field mode control

Traditional analysis on stereophonic and multichannel sound is based on localization theorem of virtual source, which serves as the basis for designing loudspeaker configuration and signal mixing. However, this traditional theorem is unable to fully explain some psychoacoustic phenomena in reproduction. In present work, a method of analyzing the control of sound field modes in stereophonic and multichannel sound reproduction is proposed. Using Fourier-Bessel expansion, the reproduced sound field is decomposed into a combination of multi-pole modes with various orders. A result consistent with that of traditional virtual source localization theorem is obtained by matching the reproduced modes with that of target sound field up to the first order. By analyzing the contributions of the power of loudspeaker signals to desired and undesired sound field modes, a cost function for desired sound field modes is introduced and serves as a physical criterion of sound field control. Analyses on examples of stereophonic and 5.1-channel sound indicate that an excessive span between a pair adjacent loudspeakers and out-of phase signals for creating virtual source outside the loudspeaker span increase the cost of sound field control, resulting in directional distortion or instability of virtual source. The analyses are validated by psychoacoustic experiments.