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The optimum signal and receiving filters for a data transmission system with a fixed channel and detection process are found. The criteria of optimality are: (i) the minimization of mean square error between the input multilevel data signal and the output to the decision threshold and (ii) the minimization of noise power output with no intersymbol interference. Explicit frequency characteristics are obtained for the separate and joint signal and receiver optimization problems. For the joint problem it is seen that some freedom exists in assigning phases to the transmitter and receiver. In addition, explicit equations are obtained for the output signal-to-noise ratio for the problems considered. The optimization procedures are carried out in detail in some examples. In comparing binary and correlative multilevel signalling (e.g., duobinary), it is seen that there may be channels for which the optimum multilevel system is superior to the optimum binary system.
J. W. Smith (Wed,) studied this question.
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