Design of digital allpass networks based on the eigenvalue problem

Abstract

AbstractThis paper presents a new method of the phase design for the digital allpass network utilizing the eigenvalue problem. The proposed design method considers the phase error between the phase response of the allpass network to be realized and the ideal phase response. The design problem is formulated as an eigenvalue problem based on the Remez algorithm. By calculating the eigenvector corresponding to the maximum eigenvalue, the filter coefficients are determined and the optimal approximate solution is obtained by iterative calculation.In the design method, the eigenvector corresponding to the maximum eigenvalue is calculated to determine the filter coefficients so that the phase error is minimized. Consequently, the convergence of the design algorithm is guaranteed. Usually, the optimal approximate solution is obtained by several times of iterations. The error‐ratio of the phase characteristics can be set arbitrarily, and the stability of the filter is ensured.Finally, the method is extended to the phase design for the digital allpass network with complex coefficients, several design examples are shown, and the usefulness of the proposed design method is demonstrated.