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Broadband beamformers are known to be highly sensitive to the errors in microphone array characteristics, especially for small-sized microphone arrays. This paper proposes an algorithm for the design of robust broadband beamformers with passband shaping characteristics using Tikhonov regularization method by taking into account the statistics of the microphone characteristics. To facilitate the derivation, a weighted least squares based broadband beamforming algorithm with passband shaping characteristics is also proposed, while keeping a minimal stopband level. Unlike the existing criteria for broadband beamforming for microphone arrays, the proposed approaches fully exploit the degrees of freedom in weighting functions of the criteria used to design broadband beamformers. By doing so, efficient and flexible broadband beamforming can be achieved with the desired passband shaping characteristics. In addition, this paper also shows that the robust broadband beamforming using the statistics of the microphone characteristics recently proposed (Doclo and Moonen, 2003 and 2007) belongs to the class of white noise gain constraint-based techniques, which gives an insight into the nature of the state-of-the-art approach. The performance of the proposed beamforming algorithms is illustrated by the design examples and is compared with the existing approaches for microphone arrays.