Transfer Matrices Decomposition With Bezout Theorem

Abstract

This letter introduces a novel method for decomposing high-order filter transfer matrices using the Bezout theorem, ensuring numerical stability. By employing polynomial division and remainder calculations, it circumvents the errors associated with evaluating high-order polynomials. Furthermore, since the extraction process involves updating the reciprocity equation, the numerical errors introduced at each step do not accumulate, ensuring a stable process. This letter outlines the extraction process for each element within the extracted pole (EP) filter and validates the proposed approach’s effectiveness and numerical stability by synthesizing a 16th-order dual-band filter with seven transmission zeros. Through error analysis, this letter quantitatively assesses the error levels of various methods, underscoring the substantial benefits of the proposed method.