This paper presents a direct formula for reproducing a sound field consisting of higher-order circular harmonics with polar phase variation. Sound fields with phase variation can be used for synthesizing various spatial attributes, such as the perceived width or the location of a virtual sound source. To reproduce such a sound field using a linear loudspeaker array, the driving function of the array is derived in the format of an integral formula. The proposed function shows fewer reproduction errors than a conventional formula focused on magnitude variations. In addition, analysis of the sweet spot reveals that its shape can be asymmetric, depending on the order of harmonics. (C) 2015 Acoustical Society of America
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