Transmission of a time-discrete message over a time-continuous channel is considered. The channel is assumed to be stationary and Gaussian. The following results are shown. 1) An optimum receiver will always contain a matched matrix filter followed by a sampling unit. 2) Jointly optimized transmitting and receiving filters will always be strictly band limited to a set of Nyquist domains. It is shown that both these results are true for any kind of message and under any measure of performance. On the basis of these results a general time-discrete matrix channel equivalent to the original time-continuous scalar channel is derived. The significance of the results is that any optimization of transmitter and receiver is reduced from a time-continuous problem to a time-discrete one.

A hybrid digital transmission system of the kind originally proposed by Chang and Freeny [4], [6] is considered. Based on predictions about cable and repeater costs around 1980, an investigation of a certain economic measure of goodness is performed. Specifically, the influence on the system cost of the choice of certain fundamental system parameters like repeater spacing, symbol rate, and number of signal levels is studied.