Efficient Design of IIR Filters with A New Positive Realness based Stability Constraint

Shishu Yin*, Yue Wu ,Hao Chang

Dept. of Electronic and Information Engineering, Anhui Finance and Economics University, Bengbu, China

Abstract: A new positive-realness based stability constraint for IIR filters is proposed. Compared to the well-known PR-based condition: {  , for  , where   is a small positive value}, the proposed constraint offers more good choices for the design of stable IIR filters, since only one case of the denominator is excluded where the denominator is in linear phase and the phase spectrum is   ｏｒ  . With the stability constraint, the design of IIR filters is formulated into a minimax optimization problem which can be solved by a CVX-based procedure. Filters so obtained are guaranteed to be stable and have an approximately equal ripple stopband magnitude response. Examples and comparisons are given to show the effectiveness of the proposed methods.

Keywords: IIR filters; Minimax; Convex optimization; Stability constraint.