Block transmission has recently been considered as an alternative to the conventional continuous transmission technique. In particular, block transmission techniques with zero padding (ZP) and cyclic prefix (CP) are becoming attractive procedures for their ability to eliminate both inter-symbol interference (ISI) and inter-block interference (IBI). In this paper, we present a unified approach to blind channel estimation and interference suppression for block transmission using ZP or CP in both single-carrier (SC) and multicarrier (MC) systems. Our approach uses a generalized multichannel minimum variance principle to design an equalizing filterbank. Channel estimate is then obtained from an asymptotically tight lower bound of the filterbank output power. Numerical examples show that the proposed schemes approach the CRB as the signal-to-noise ratio (SNR) increases. Additionally, they exhibit low sensitivity to unknown narrowband interference and compare favorably with subspace blind channel estimators.