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This paper deals with the joint optimization of transmitting and receiving filters in multiplex transmission of pulse-amplitude-modulated (PAM) signals. A mean-square-error criterion is used. The signal processes are assumed to be mutually uncorrelated and with equal power spectral densities. Transfer matrix functions for the transmitting and for the receiving filters are used as an expedient tool. It is shown that optimal multiplexing systems can be achieved with a bandwidth of . The transfer matrix functions of optimal transmitters (and corresponding optimal receivers) are defined up to premultiplication by an arbitrary unitary matrix function. This provides for freedom of choice between various multiplexing techniques like frequency-domain multiplexing, time-domain multiplexing, or combinations thereof.