A CHEBYSHEV-APPROXIMATION OF THE FREQUENCY RESPONSES OF NONRECURSIVE DIGITAL CORRECTORS

Correctors are designed to reproduce, with a given accuracy, required amplitude-frequency responses (AFR) A0(omega) and phase-frequency responses (PFR) theta0(omega) within a frequency band omega1 less-than-or-equal-to omega less-than-or-equal-to omega2. An optimal solution of the approximation problem when synthesizing analog correctors was given [3, 5]. The synthesis of harmonic correctors whose frequency responses are described by the same functions as used for nonrecursive digital correctors (NDC) and filters is considered in [2, 4]. It is only necessary to substitute the sampling interval T for the delay T in one branch of the delay line. The methods proposed in [2, 3, 4, 5] as well as those presented in [1, 6] do not enable solutions of the approximation problem to be obtained that are optimal in the minimax sense. The purpose of this paper is to solve the problem of an approximation of the frequency responses of an NDC for a Chebyshev criterion of closeness between the approximated and the approximating functions.