A DESIGN METHOD FOR 1-D IIR FILTERS WITH A NECESSARY AND SUFFICIENT STABILITY CRITERION

In general, it is necessary to guarantee stability when designing of One-dimensional (1-D) infinite impulse response (IIR) filters. Methods for guaranteeing stability by using Rouche's theorem, the positive realness condition, or a method based on the positive realness have previously been proposed for defining the necessary iterative approximation algorithm. In these cases, the conventional stability criteria become the sufficient condition to guarantee stability. As a result, the stability domains obtained using these criteria are narrow and variable. In the present paper, we propose a design method of 1-D IIR filters, which applies a stability criterion based on the system matrix to the successive projection (SP) method. The stability criterion based on the system matrix in the proposed method becomes the necessary and sufficient condition for guaranteeing stability. Therefore, the stability domain does not depend on denominator polynomial coefficients, and the domain is not variable. Moreover, the stability domain is wider than that by the conventional stability criteria. As a result, 1-D IIR filters obtained using the proposed method have a smaller ripple than those from using conventional methods. In addition, the proposed design method realizes faster design times than those from using the conventional design methods.