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Recently, the use of redundant memoryless single-carrier transmitters has been reported as an efficient choice to reduce distortions introduced by finite-impulse response (FIR) channels. In this work, redundant FIR transceivers are proposed to address not only channel frequency selectivity but additive colored noise, which strongly degrades the performance of memoryless transceivers. The transmitter is shown to be paraunitary, resulting in a simple receiver. The proposed system is optimized like a modulated filter bank. Channel shortening and post-combiner equalizers are used to improve system performance. Comparisons with recent proposed schemes are presented, illustrating the efficiency of the new structure for selective channels with colored noise.