A weighted least-squares method for the design of stable 1-D and 2-D IIR digital filters

In this paper, we present a new approach to the least-squares design of stable infinite impulse response (IIR) digital filters, The design is accomplished by using an iterative scheme in which the denominator polynomial obtained from the preceding iteration is treated as a part of the weighting function, and each iteration is carried out by solving a standard quadratic programming problem that yields a stable rational function, When the iteration converges, a stable and truly least-squares solution is obtained. The method is then extended to address the least-squares design of stable IIR two-dimensional (2-D) filters, Examples are included to illustrate the proposed design techniques.