In this paper, we propose a novel method of sound field reproduction using a microphone array and loudspeaker array. Our objective is to obtain the driving signal of a planar or linear loudspeaker array only from the sound pressure distribution acquired by the planar or linear microphone array. In this study, 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 a mean of a filter in a spatio-temporal frequency domain. Numerical simulation results are presented to compare the proposed method with the method based on the conventional least square algorithm. The reproduction accuracies were found to be almost the same, however, the filter size and amount of calculation required for the proposed method were much smaller than those for the least square algorithm based one.