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In this paper, we propose an unconstrained IIR digital filter design method in the weighted least-squares (WLS) sense. Unlike some other design methods which utilize approximation techniques to simplify the nonlinear approximation error functions, this method expresses the design problem strictly, and utilizes the general-purpose optimization algorithms to find the minimum point. In order to guarantee the stability of designed filters, a stability criterion is developed from the argument principle of complex analysis. Unlike other frequency-domain stability criteria, it is both sufficient and necessary. Two examples are also presented to demonstrate the effectiveness of the proposed method.