On optimal filters with maximum number of constraints on amplitude and phase characteristics. (English) Zbl 0883.93055

The paper presents a complete definition of the optimal solution for filters with amplitude and phase (or delay) specifications on general interpolation bases. Constant or arbitrarily prescribed lowpass or bandpass group delay and amplitude characteristics are approximated in the maximally flat, ripple or mixed sense for lumped filters; highpass and band rejection characteristics are also considered for distributed or sampled data filters. Approximations for reciprocal reactant and non-reciprocal realizations are considered. The relationship between the number of free parameters and the number of amplitude and phase constraints for a given degree is derived for the non-reciprocal as well as for the reciprocal lossy and the reciprocal reactant cases. Necessary conditions for stability and monotonicity in the transition band of non-reciprocal and reciprocal reactant transfer functions are proposed. Finally, some approximation methods are compared and evaluated from the optimality, stability and monotonicity points of view.
Reviewer: S.Curteanu (Iaşi)


93E11 Filtering in stochastic control theory
93D21 Adaptive or robust stabilization
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