We propose a filter design method for a circular loudspeaker array. This method is based on extended three-dimensional (3-D) bases that are observed by driving each circular harmonic mode using a prototypical circular loudspeaker array. When a desired 3-D directivity pattern is expanded by the extended 3-D bases, the filter coefficients can be obtained by combining the circular harmonics with the expansion coefficients of the desired 3-D directivity pattern. Moreover, the proposed method can suppress large filter gains at low frequencies by limiting the gain at each order (mode) using L1-norm optimization. We evaluated the performance of directivity and sound distortion using an actual 8-element circular loudspeaker array of radius 0.054 m. These results showed that the proposed method could control the 3-D directivity with little distortion.
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