Design of hybrid filter banks using norm performance measures

This study presents H_∞ norm and mixed H₂/H_∞ norm optimal designs of digital synthesis filters of a hybrid filter bank. The problem for designing finite-impulse response (FIR) synthesis filters is cast as a H_∞ optimisation or mixed H₂/H_∞ optimisation problem by constructing a hybrid-induced error system. Both the problems can be solved using the theory of linear matrix inequalities such that FIR filters are directly obtained without truncation of infinite impulse responses. Two design examples are provided to illustrate the effectiveness of the proposed approaches.