Reply to "Comments on 'A weighted least-squares method for the design of stable 1-D and 2-D IIR digital filters'"

A recent iterative procedure by Lu et al. for designing IIR filters is recognized as the Sanathanan–Koerner or Steiglitz–McBride iteration, which was proposed originally in 1963 and 1965, respectively, for system identification purposes. We re-examine some claims and issues related to Lu et al.’s paper1 in view of various properties that have been deduced for the Steiglitz–McBride iteration in the identification literature. In particular, the Steiglitz–McBride procedure is known not to minimize a least-squares distance measure, contrary to Lu et al.’s claim. It can, however, provide good models and remain stable during successive iterations under specific conditions which are reviewed within.