Transmitter redundancy introduced using filterbank precoders generalizes existing modulations including OFDM, DMT, TDMA, and CDMA schemes encountered with single- and multiuser communications. Sufficient conditions are derived to guarantee that with FIR filterbank precoders FIR channels are equalized perfectly in the absence of noise by FIR zero-forcing equalizer filterbanks, irrespective of the channel zero locations. Multicarrier transmissions through frequency-selective channels can thus be recovered even when deep fades are present. Jointly optimal transmitter-receiver filterbank designs are also developed, based on maximum output SNR and minimum mean-square error criteria under zero-forcing and fixed transmitted power constraints. Analytical performance results are presented for the zero-forcing filterbanks and are compared with mean-square error and ideal designs using simulations.