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In this paper, the problem of designing finite-impulse-response (FIR) equalizers for multiple-input multiple-output (MIMO) FIR channels is considered. It is shown that an arbitrary MIMO frequency-selective channel can be rendered FIR equalizable by a suitable filter bank (FB) precoding operation that introduces redundancy at the transmitter. The expression for the minimum redundancy required to ensure FIR invertibility is derived. The analysis is extended to the case of MIMO multicarrier modulation. Optimum zero-forcing (ZF) and minimum mean-squared error (MMSE) solutions for the FIR equalizer are derived. Simulation results are provided to demonstrate that the proposed scheme achieves better performance than the block-processing methods while supporting a higher data rate.