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Sound reproduction systems aim to produce a desired sound field over a region of space. At high frequencies, the number of loudspeakers required is prohibitive. This paper shows that the use of Nth order loudspeakers, in which each loudspeaker produces polar responses up to cos(Nφ) and sin (Nφ) , produces accurate reproduction over N times the area of a first order array and can largely eliminate any exterior field. This allows a significant reduction in the number of loudspeaker units, at the expense of increased complexity in each loudspeaker unit.