Optimum Linear Shaping and Filtering Networks

Optimum transmitter and receiver transfer characteristics are obtained for linear communication systems under assumptions of fixed power levels and fixed over-all distortion of message signal. Two separate criteria of performance are used as the basis for optimization: (a) the mean-square value or variance of the receiver output noise component and (b) the probability that the noise component of receiver output exceeds a preassigned tolerance value at least once during some finite period of observation.