Weighted least squares IIR filter design with arbitrary magnitude and phase responses and specified stability margin

This paper presents a new approach to the frequency domain design of infinite impulse response (IIR) digital filters with arbitrary magnitude and phase responses and a constraint on the maximum pole radius. The proposed method uses the polynomial coefficients of the filter's transfer function as design parameters which provides better solutions in most cases than other parameterizations of the transfer function. An arbitrarily specified constraint on the pole radii can be satisfied using the implications of Rouche's theorem. Using these results we modify a standard method for the solution of nonlinear least squares problems to incorporate this maximum pole radius constraint which we consider to be important for implementing the filter with finite wordlength. A design example demonstrates the superiority of the proposed method over two other methods considering the same design problem.