The problem of reproducing J signals with K loudspeakers is considered. A algebraic, time-domain synthesis approach is developed that extends the multi-input multi-output inverse theorem (MINT) of Miyoshi and Kaneda. The approach is general and can encompass joint surround sound synthesis and loudspeaker/room correction. First, a discrete time-domain matrix description is developed that captures the effects of amplifiers, loudspeakers, and room acoustics. Based on this model, it is shown that exact synthesis is possible with practical reproduction apparatus only if K>J. Sufficient conditions that are based on impulse responses are also presented. The results are specialized to the case of zero-crosstalk transaural sound reproduction, and the theoretical importance of loudspeaker time alignment is illustrated. Finally, minimum-power exact synthesis is briefly described.
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