远场波束形成问题的光滑过渡带设计及分析

Smooth Transition Region Design and Analysis of the Far-Field Beamformer Problem

麦克风阵列宽带波束形成的设计是一个优化问题,它在语音信号处理中的应用非常广泛.它的目标函数通常只考虑了通带区域和阻带区域,在过渡带区域不受限制.当滤波器长度比较大时,问题最优解的实际响应函数在过渡带区域出现振荡,这使得麦克风阵列系统在不确定环境下的鲁棒性非常差.本文通过对波束形成设计问题进行改进,使得当滤波器长度充分大时,实际响应函数在过渡带区域实现平稳光滑过渡,并且与原波束形成设计的性能非常接近.此外,本文给出了波束形成设计与光滑过渡带设计的性能分析,并通过数值例子验证了光滑过渡带设计的有效性.

Broadband beamformer design of microphone array is an optimization problem,which has wide applications in acoustic signal processing. In general,only the passband region and the stopband region are considered in the objective function,while it is not constrained in the transition region,Then,the actual response function of the optimal solution will show serious vibration in the transition region when the filter length is large enough. This causes a poor robustness of the microphone array system in an uncertain environment. In this paper,we consider this problem. By modifying the original problem,the actual response function becomes very smooth in the transition region,while the performance of the design remains unaffected. We analyze the optimal solutions of the original problem and the modified problem and verify the effectiveness of the modified problem with a numerical example.