We previously proposed an optimal (in the maximum likelihood sense) convolutional beamformer that can perform simultaneous denoising and dereverberation, and showed its superiority over the widely used cascade of a WPE dereverberation filter and a conventional MPDR beamformer. However, it has not been fully investigated which components in the convolutional beamformer yield such superiority. To this end, this paper presents a new derivation of the convolutional beamformer that allows us to factorize it into a WPE dereverberation filter, and a special type of a (non-convolutional) beamformer, referred to as a wMPDR beamformer, without loss of optimality. With experiments, we show that the superiority of the convolutional beamformer in fact comes from its wMPDR part.
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