Determination of Minimax Design of Multiple-Resonator-based Harmonic Estimators through Linear Programming

The multiple-resonator (MR) filter structure has been proposed in previous works as a convenient approach to the dynamic harmonic analysis. This method, by using a parallel structure with common feedback, is very robust and, in addition, allows a reduction of the computational burden. The objective of this article is to determine the design algorithms which simultaneously assure: i) the quasi-equiripple minimax frequency response in stopband(s), ii) the wide flat-top amplitude response in the passband, and iii) the reduced group delay, which is often requested in standards. In this article, an optimized postprocessing compensation filters are applied to obtain the desired frequency responses convenient for fast measurements in the dynamic conditions. A linear-programming-based optimization design method is applied. This way, both the flatness in the passband and the attenuation in the stopband are significantly improved simultaneously. Three different optimization criteria are formulated, and design examples with obtained results are presented. The proposed method has been investigated for up to 64 harmonics, under different conditions, and confirmed to be valuable and efficient tool for harmonic components estimation.