In block transmission systems, transmitter-induced redundancy using finite-impulse response (FIR) filterbanks can be used to suppress intersymbol interference and equalize FIR channels irrespective of channel zeros. At the receiver end, linear or decision-feedback (DF) FIR filterbanks can be applied to recover the transmitted data. Closed-form expressions are derived for the FIR linear or DF filterbank receivers corresponding to varying amounts of transmission redundancy. Our framework encompasses existing block transmission schemes and offers low implementation-cost equalization techniques both when interblock interference is eliminated, and when IBI is present as, e.g., in orthogonal frequency-division multiplexing with insufficient cyclic prefix. By applying blind channel estimation methods, our filterbank transmitters-receivers (transceivers) dispense with bandwidth consuming training sequences. Extensive simulations illustrate the merits of our designs.