A sequential minimization procedure for least-squares design of stable IIR filters

Since infinite impulse response (IIR) digital filters do not have intrinsic stability, one of the main problems needed to be considered in their optimal designs is to choose proper stability constraints to insure the stability of the designed filters. The stability-triangle based conditions are necessary and sufficient as well as linear conditions for the stability of IIR filters. In order to make good use of these conditions, a second-order factor based sequential minimization procure is used to convert the least-squares design of an IIR digital filter into a sequence of least-squares sub-problems, each of which optimizes the whole numerator but only one second-order denominator factor while keeping all other denominator factors unchanged. Design examples show that the proposed procedure may obtain much better lease-squares filters.