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We derive conditions on the impulse response and input signal of a frequency-selective finite-impulse response channel to be diagonalized by the discrete cosine transform (DCT) into parallel, decoupled, and memoryless subchannels. We show how these conditions can be satisfied in a practical multicarrier transceiver through a novel design of the guard sequence and the front-end prefilter. This DCT-based design results in complete elimination of interblock and intercarrier interference without channel knowledge at the transmitter and at the same guard sequence overhead, compared with DFT-based multicarrier transceivers. Extensions to multiinput multioutput frequency-selective channels are also described. Finally, we present numerical examples from wireline and wireless communications scenarios to illustrate the viability and practicality of the DCT as a modulation/demodulation basis for baseband and passband signaling over frequency-selective channels.