Efficient WLS Design of IIR Digital Filters Using Partial Second-Order Factorization

In this brief, a novel algorithm is developed for the design of infinite-impulse-response digital filters in the weighted least-squares sense. To simplify the design problem, the Levy linearized function and the Sanathanan-Koerner iterative technique are utilized. In the proposed algorithm, a denominator polynomial is decomposed as a cascade of a few second-order factors (SOFs) and a higher order factor (HOF). They are sequentially updated in each iteration. When updating SOFs composed of poles that are tending to be outside the unit circle, necessary and sufficient stability conditions are taken into account, while the HOF is optimized without any stability constraint. The number of SOFs can be automatically determined in the proposed design procedure, which is convenient for practical designs. Simulation results demonstrate that the proposed algorithm can attain a balance between computational efficiency and design accuracy.