Design of Infinite Impulse Response (IIR) filters with almost linear phase characteristics

We propose a method for designing Infinite Impulse Response (IIR) filters with specified magnitude frequency-response tolerances and approximately linear phase characteristics. The design method consists of two steps. First, a Finite Impulse Response (FIR) filter with linear phase is designed using standard optimisation techniques (e.g. linear programming). In the second stage, the designed FIR filter is approximated by a stable IIR filter using a Hankel-norm approximation method. This is based on a recent technique for approximating discrete-time descriptor systems and requires only standard linear algebraic routines, while avoiding altogether the solution of two matrix Lyapunov equations which is computationally expensive. A-priori bounds on the magnitude and phase errors are obtained which may be used to select the lowest-order IIR filter order which satisfies the specified design tolerances. The efective-ness of the method is illustrated with a numerical example.