Directivity control for regular polyhedron loudspeaker array based on weighted least-squares method using adjusted weight in spherical harmonics domain

Abstract

We propose an adjusted weight least-squares method for directivity control of spherical loudspeaker arrays in the spherical harmonics domain. In previous work, we demonstrated that the sidelobes of the directivity pattern can be suppressed using the weighted least-squares method in the frequency domain. However, the gains of the calculated filter coefficients were very large at low frequencies. Consequently, to overcome this problem, we designed filter coefficients in the spherical harmonic domain. First, we set an ideal directivity pattern using a window function. Next, we obtain the filter based on the weighted least-squares method in the spherical harmonic domain with an initial weighting factor. Then, we update the weighting factor only on the side opposite that being faced based on the difference in sound pressure level between the ideal and the simulated radiation patterns. We then repeat this process until the difference level is satisfied by the condition of the update. The results of comparison of our proposed method with our previous method and the conventional least-squares method indicate that although the beam width in the look direction is wider than our previous method, our proposed method effectively prevents increasing filter coefficients by limiting order at low frequencies.