An efficient equalization filter design approach for the accurate sound reproduction in a room environment with wide-band content

Abstract

In some sound reproduction applications, a desired sound field needs to be reproduced by remote loudspeakers in a room with sufficient accuracy over a wide frequency band. When low-frequency room modes exist and the low-frequency content is required to be reproduced accurately, an equalization filter with a long time-domain response may be necessary, resulting in a filter with a significantly high filter order, especially when the sampling rate is high for the high-frequency content. This imposes computational challenges on both filter design and implementation. In this article, a convex formulation is proposed for the wide-band sound reproduction filter design. To address issues due to the low-frequency room modes, a reduced-order technique is then proposed based on a sub-band filter structure where a low sampling rate is used to equalize the low-frequency room mode characteristics, and a high sampling rate is used for high-frequency features which usually has a short time span in response. The computational time can be reduced by several orders of magnitude and the numerical stability can be improved when the proposed order reduction method is used to eliminate redundant orders. Simulation and experimental results confirm the accuracy and efficiency advantages of the proposed method.