Synthesis of optimum single-channel discrete signals and filters

Synthesis of optimum discrete signals and filters for single-channel processing, specifically signals with linear frequency-modulation of the phase, is considered on the basis of the quadratic optimality criterion. In the case of signals with a reciprocal indeterminacy function, the problem reduces to finding the complex signal and filter envelopes which will maximize the crest-to-valley ratio in the time-frequency plane. The most typical five variants of the problem are: (1) with the signal vector given, find the filter vector which maximizes that ratio; (2) find both signal and filter vectors which will maximize that ratio; (3) with absolute values of the signal given, find both signal and filter vectors which will maximize that ratio; (4) with the filter matched to the signal, find the signal vector which maximizes that ratio; and (5) with the filter matched to the signal and absolute values of the signal given, find the signal vector which will maximize that ratio. A suboptimum procedure is proposed for solving these problems, a procedure less unwieldy than optimal solution and based on minimization of the proximity criterion. As such a criterion is regarded the distance between the law of signal phase modulation and the sought signal in the L(2) space.