Directivity control of a compact circular loudspeaker array based on selected orders of circular harmonic expansion

Abstract

We investigated directivity control of a compact circular loudspeaker array that can be attached to the arm. The loudspeaker array can be used for various wearable systems, such as personal audio reproduction systems. A personal audio system often requires that sound leakage outside the listening area in three-dimensional space be minimized. Digital filters that control directivity are usually designed using the multi-point control method. However, the multi-point method causes large filter gains at low frequencies, owing to unstable inverse matrix calculation, which results in sound distortion during practical use. Many methods that use a regularization parameter to overcome the unstable inverse matrix have been proposed; however, they are difficult to apply directly. Thus, after studying the relationship between orders of circular harmonic expansion and filter gain, we propose a stable digital filter design based on appropriately selected orders of circular harmonic expansion for each frequency band. Directivity simulations conducted using the measured circular loudspeaker array response based on the proposed method indicate that the proposed method achieves a more stable filter gain than the multi-point control method. Further, it controls three-dimensional directivity by sacrificing a narrow directivity at low frequencies.