Robust Synthesis of Multiband Filters Based on Transmission Zero Redundancy Method

This letter proposes the robust synthesis of low-pass polynomials for multiband filters with different equiripple levels, independent orders, and pass ranges, which is robust for very special cases not available in previous works. The synthesis is carried out by introducing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> redundant transmission zeros (TZs) into the low-pass filtering function with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> subbands. The redundant TZs, either real or complex in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega $</tex-math> </inline-formula>-domain, are properly managed (via extra parameters) and then iterated (using Remez-like algorithm) together with equiripple points to satisfy the prescribed responses. In consequence, the convergence condition of iterations is considerably improved compared to previous works, due to diverse allocations of redundant TZs. For validation, we demonstrate synthesis examples and confirm reasonable responses, which are not achieved before, revealing the effectiveness and robustness of the proposed method.