Design of low-order linear-phase IIR filters via orthogonal projection

This paper presents an indirect linear-phase IIR filter design technique based on a reduction of linear-phase FIR filters. The desired filter is obtained by minimizing the L₂ norm of the difference between the original FIR filter and the lower order IIR filter. We first establish a relationship between the Hankel singular values of the discarded part of the FIR filter and the L₂ norm of the corresponding filter approximation error based on model truncation. This result motivates us to propose a simple finite search method that will achieve better approximation results than commonly used truncation methods such as the balanced truncation (BT) and the impulse response gramian (IRG) methods. We then develop an iterative algorithm for finding an optimal IIR filter based on a matrix projection of the original FIR filter. The convergence of the proposed algorithm is established. Filters designed using the proposed algorithm are compared with those obtained by other techniques with respect to the amplitude response and group delay characteristics in the passband. Numerical examples show that the proposed algorithm offers the best performance