A method of transform from the received signals of a microphone array to the driving signals of a loudspeaker array for sound field reproduction is investigated. Our objective is to obtain the driving signal of a planar or linear loudspeaker array only from the sound pressure distribution acquired by a planar or linear microphone array. We derive a formulation of the transform from the received signals of the microphone array to the driving signals of the loudspeaker array. The transform is achieved as the mean of a filter in a spatio-temporal frequency domain. Results of measurement experiments in an anechoic room are presented to compare the proposed method with the method based on the conventional least mean square algorithm. The reproduction accuracies were found to be almost the same, but the filter size and amount of calculation required for the proposed method were much smaller than those for the least mean square algorithm based one.
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