Design of IIR digital allpass filters based on eigenvalue problem

A new method is proposed for designing IIR digital allpass filters with an equiripple phase response that can be proven to be optimal in the Chebyshev sense. The proposed procedure is based on the formulation of an eigenvalue problem by using the Remez exchange algorithm. Since there exists more than one eigenvalue in the general eigenvalue problem, we introduce a new and very simple selection rule for the eigenvalue to be searched for, where the rational interpolation is performed if and only if the real maximum eigenvalue is chosen. Therefore, the solution of the rational interpolation problem can be gotten by computing only one eigenvector corresponding to the real maximum eigenvalue, and the optimal filter coefficients are easily obtained through a few iterations without any initial guess of the solution. The design algorithm proposed in this correspondence not only retains the speed inherent in the Remez exchange algorithm but also simplifies the interpolation step because it has been reduced to the computation of the real maximum eigenvalue. Two examples are designed to demonstrate the effectiveness of this method.