Closed form expressions of the minimum L2-sensitivity realizations for all-pass digital filters
Shunsuke Yamaki, Masahide Abe, Masayuki Kawamata · 2010 2nd IEEE InternationalConference on Network Infrastructure and Digital Content · 2010
This paper presents closed form expressions of the minimum L2-sensitivity realizations of all-pass digital filters. We first prove that the L2-sensitivity minimization problem can be solved analytically if the all second-order modes of a digital filter are equal. We focus on the fact that the second-order modes of all-pass digital filters are all unity. As a result, it is clarified that the minimum L2-sensitivity realization of an all-pass digital filter is equal to the balanced realization, of which closed form expression can be derived analytically.