Design of IIR digital filters with finite-wordlength coefficients based on a MLS criteria

In this paper, we treat a design method for IIR digital filters with finite-wordlength described by rational transfer functions. First, we form the filter design problem in the quadratic form with respect to the numerator and denominator coefficients using the modified least-squares (MLS) criterion. Next, we show the lower bound estimation principle using the Lagrange multiplier method in order to search for the optimum solution of the filters efficiently. Additionally we can check the filter stability when designing the denominator coefficients. Finally, we show the effectiveness of the proposed method using a numerical example.