This paper presents new filter bank design methods for sub- band adaptive beamforming. In this work, we design analysis and synthesis prototypes for modulated filter banks so as to minimize each aliasing term individually. We then drive the total response error to null by constraining these prototypes to be Nyquist(M) filters. Thereafter those modulated filter banks are applied to a speech separation system which extracts a target speech signal. In our system, speech signals are first transformed into the subband domain with our filter banks, and the subband components are then processed with a beamforming algorithm. Following beamforming, post-filtering and binary masking are further performed to remove residual noises. We show that our filter banks can suppress the residual aliasing distortion more than conventional ones. Furthermore, we demonstrate the effectiveness of our design techniques through a set of automatic speech recognition experiments on the multi-channel speech data from the PASCAL Speech Separation Challenge. The experimental results prove that our beamforming system with the proposed filter banks achieves the best recognition performance, a 39.6 % word error rate (WER), with half the amount of computation of that of the conventional filter banks while the perfect reconstruction filter banks provided a 44.4 % WER.